diff --git a/previews/PR41/assets/documenter.js b/previews/PR41/assets/documenter.js
new file mode 100644
index 0000000..6adfbbb
--- /dev/null
+++ b/previews/PR41/assets/documenter.js
@@ -0,0 +1,331 @@
+// Generated by Documenter.jl
+requirejs.config({
+  paths: {
+    'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia.min',
+    'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min',
+    'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.min',
+    'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/contrib/auto-render.min',
+    'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min',
+    'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min',
+    'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min',
+    'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/highlight.min',
+    'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia-repl.min',
+  },
+  shim: {
+  "highlight-julia": {
+    "deps": [
+      "highlight"
+    ]
+  },
+  "katex-auto-render": {
+    "deps": [
+      "katex"
+    ]
+  },
+  "headroom-jquery": {
+    "deps": [
+      "jquery",
+      "headroom"
+    ]
+  },
+  "highlight-julia-repl": {
+    "deps": [
+      "highlight"
+    ]
+  }
+}
+});
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) {
+$(document).ready(function() {
+  renderMathInElement(
+    document.body,
+    {
+  "delimiters": [
+    {
+      "left": "$",
+      "right": "$",
+      "display": false
+    },
+    {
+      "left": "$$",
+      "right": "$$",
+      "display": true
+    },
+    {
+      "left": "\\[",
+      "right": "\\]",
+      "display": true
+    }
+  ]
+}
+
+  );
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) {
+$(document).ready(function() {
+    hljs.highlightAll();
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require([], function() {
+function addCopyButtonCallbacks() {
+  for (const el of document.getElementsByTagName("pre")) {
+    const button = document.createElement("button");
+    button.classList.add("copy-button", "fas", "fa-copy");
+    el.appendChild(button);
+
+    const success = function () {
+      button.classList.add("success", "fa-check");
+      button.classList.remove("fa-copy");
+    };
+
+    const failure = function () {
+      button.classList.add("error", "fa-times");
+      button.classList.remove("fa-copy");
+    };
+
+    button.addEventListener("click", function () {
+      copyToClipboard(el.innerText).then(success, failure);
+
+      setTimeout(function () {
+        button.classList.add("fa-copy");
+        button.classList.remove("success", "fa-check", "fa-times");
+      }, 5000);
+    });
+  }
+}
+
+function copyToClipboard(text) {
+  // clipboard API is only available in secure contexts
+  if (window.navigator && window.navigator.clipboard) {
+    return window.navigator.clipboard.writeText(text);
+  } else {
+    return new Promise(function (resolve, reject) {
+      try {
+        const el = document.createElement("textarea");
+        el.textContent = text;
+        el.style.position = "fixed";
+        el.style.opacity = 0;
+        document.body.appendChild(el);
+        el.select();
+        document.execCommand("copy");
+
+        resolve();
+      } catch (err) {
+        reject(err);
+      } finally {
+        document.body.removeChild(el);
+      }
+    });
+  }
+}
+
+if (document.readyState === "loading") {
+  document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks);
+} else {
+  addCopyButtonCallbacks();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) {
+
+// Manages the top navigation bar (hides it when the user starts scrolling down on the
+// mobile).
+window.Headroom = Headroom; // work around buggy module loading?
+$(document).ready(function() {
+  $('#documenter .docs-navbar').headroom({
+    "tolerance": {"up": 10, "down": 10},
+  });
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Modal settings dialog
+$(document).ready(function() {
+  var settings = $('#documenter-settings');
+  $('#documenter-settings-button').click(function(){
+    settings.toggleClass('is-active');
+  });
+  // Close the dialog if X is clicked
+  $('#documenter-settings button.delete').click(function(){
+    settings.removeClass('is-active');
+  });
+  // Close dialog if ESC is pressed
+  $(document).keyup(function(e) {
+    if (e.keyCode == 27) settings.removeClass('is-active');
+  });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Manages the showing and hiding of the sidebar.
+$(document).ready(function() {
+  var sidebar = $("#documenter > .docs-sidebar");
+  var sidebar_button = $("#documenter-sidebar-button")
+  sidebar_button.click(function(ev) {
+    ev.preventDefault();
+    sidebar.toggleClass('visible');
+    if (sidebar.hasClass('visible')) {
+      // Makes sure that the current menu item is visible in the sidebar.
+      $("#documenter .docs-menu a.is-active").focus();
+    }
+  });
+  $("#documenter > .docs-main").bind('click', function(ev) {
+    if ($(ev.target).is(sidebar_button)) {
+      return;
+    }
+    if (sidebar.hasClass('visible')) {
+      sidebar.removeClass('visible');
+    }
+  });
+})
+
+// Resizes the package name / sitename in the sidebar if it is too wide.
+// Inspired by: https://github.com/davatron5000/FitText.js
+$(document).ready(function() {
+  e = $("#documenter .docs-autofit");
+  function resize() {
+    var L = parseInt(e.css('max-width'), 10);
+    var L0 = e.width();
+    if(L0 > L) {
+      var h0 = parseInt(e.css('font-size'), 10);
+      e.css('font-size', L * h0 / L0);
+      // TODO: make sure it survives resizes?
+    }
+  }
+  // call once and then register events
+  resize();
+  $(window).resize(resize);
+  $(window).on('orientationchange', resize);
+});
+
+// Scroll the navigation bar to the currently selected menu item
+$(document).ready(function() {
+  var sidebar = $("#documenter .docs-menu").get(0);
+  var active = $("#documenter .docs-menu .is-active").get(0);
+  if(typeof active !== 'undefined') {
+    sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15;
+  }
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+function set_theme(theme) {
+  var active = null;
+  var disabled = [];
+  for (var i = 0; i < document.styleSheets.length; i++) {
+    var ss = document.styleSheets[i];
+    var themename = ss.ownerNode.getAttribute("data-theme-name");
+    if(themename === null) continue; // ignore non-theme stylesheets
+    // Find the active theme
+    if(themename === theme) active = ss;
+    else disabled.push(ss);
+  }
+  if(active !== null) {
+    active.disabled = false;
+    if(active.ownerNode.getAttribute("data-theme-primary") === null) {
+      document.getElementsByTagName('html')[0].className = "theme--" + theme;
+    } else {
+      document.getElementsByTagName('html')[0].className = "";
+    }
+    disabled.forEach(function(ss){
+      ss.disabled = true;
+    });
+  }
+
+  // Store the theme in localStorage
+  if(typeof(window.localStorage) !== "undefined") {
+    window.localStorage.setItem("documenter-theme", theme);
+  } else {
+    console.error("Browser does not support window.localStorage");
+  }
+}
+
+// Theme picker setup
+$(document).ready(function() {
+  // onchange callback
+  $('#documenter-themepicker').change(function themepick_callback(ev){
+    var themename = $('#documenter-themepicker option:selected').attr('value');
+    set_theme(themename);
+  });
+
+  // Make sure that the themepicker displays the correct theme when the theme is retrieved
+  // from localStorage
+  if(typeof(window.localStorage) !== "undefined") {
+    var theme =  window.localStorage.getItem("documenter-theme");
+    if(theme !== null) {
+      $('#documenter-themepicker option').each(function(i,e) {
+        e.selected = (e.value === theme);
+      })
+    } else {
+      $('#documenter-themepicker option').each(function(i,e) {
+        e.selected = $("html").hasClass(`theme--${e.value}`);
+      })
+    }
+  }
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// update the version selector with info from the siteinfo.js and ../versions.js files
+$(document).ready(function() {
+  // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the
+  // siteinfo.js file, we just return immediately and not display the version selector.
+  if (typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === 'boolean' && DOCUMENTER_VERSION_SELECTOR_DISABLED) {
+    return;
+  }
+
+  var version_selector = $("#documenter .docs-version-selector");
+  var version_selector_select = $("#documenter .docs-version-selector select");
+
+  version_selector_select.change(function(x) {
+    target_href = version_selector_select.children("option:selected").get(0).value;
+    window.location.href = target_href;
+  });
+
+  // add the current version to the selector based on siteinfo.js, but only if the selector is empty
+  if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) {
+    var option = $("<option value='#' selected='selected'>" + DOCUMENTER_CURRENT_VERSION + "</option>");
+    version_selector_select.append(option);
+  }
+
+  if (typeof DOC_VERSIONS !== 'undefined') {
+    var existing_versions = version_selector_select.children("option");
+    var existing_versions_texts = existing_versions.map(function(i,x){return x.text});
+    DOC_VERSIONS.forEach(function(each) {
+      var version_url = documenterBaseURL + "/../" + each;
+      var existing_id = $.inArray(each, existing_versions_texts);
+      // if not already in the version selector, add it as a new option,
+      // otherwise update the old option with the URL and enable it
+      if (existing_id == -1) {
+        var option = $("<option value='" + version_url + "'>" + each + "</option>");
+        version_selector_select.append(option);
+      } else {
+        var option = existing_versions[existing_id];
+        option.value = version_url;
+        option.disabled = false;
+      }
+    });
+  }
+
+  // only show the version selector if the selector has been populated
+  if (version_selector_select.children("option").length > 0) {
+    version_selector.toggleClass("visible");
+  }
+})
+
+})
diff --git a/previews/PR41/assets/logo.png b/previews/PR41/assets/logo.png
new file mode 100644
index 0000000..f1947e9
Binary files /dev/null and b/previews/PR41/assets/logo.png differ
diff --git a/previews/PR41/assets/search.js b/previews/PR41/assets/search.js
new file mode 100644
index 0000000..c133f74
--- /dev/null
+++ b/previews/PR41/assets/search.js
@@ -0,0 +1,267 @@
+// Generated by Documenter.jl
+requirejs.config({
+  paths: {
+    'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min',
+    'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min',
+    'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min',
+  }
+});
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'lunr', 'lodash'], function($, lunr, _) {
+
+$(document).ready(function() {
+  // parseUri 1.2.2
+  // (c) Steven Levithan <stevenlevithan.com>
+  // MIT License
+  function parseUri (str) {
+    var  o   = parseUri.options,
+      m   = o.parser[o.strictMode ? "strict" : "loose"].exec(str),
+      uri = {},
+      i   = 14;
+
+    while (i--) uri[o.key[i]] = m[i] || "";
+
+    uri[o.q.name] = {};
+    uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) {
+      if ($1) uri[o.q.name][$1] = $2;
+    });
+
+    return uri;
+  };
+  parseUri.options = {
+    strictMode: false,
+    key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"],
+    q:   {
+      name:   "queryKey",
+      parser: /(?:^|&)([^&=]*)=?([^&]*)/g
+    },
+    parser: {
+      strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/,
+      loose:  /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/
+    }
+  };
+
+  $("#search-form").submit(function(e) {
+    e.preventDefault()
+  })
+
+  // list below is the lunr 2.1.3 list minus the intersect with names(Base)
+  // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with)
+  // ideally we'd just filter the original list but it's not available as a variable
+  lunr.stopWordFilter = lunr.generateStopWordFilter([
+    'a',
+    'able',
+    'about',
+    'across',
+    'after',
+    'almost',
+    'also',
+    'am',
+    'among',
+    'an',
+    'and',
+    'are',
+    'as',
+    'at',
+    'be',
+    'because',
+    'been',
+    'but',
+    'by',
+    'can',
+    'cannot',
+    'could',
+    'dear',
+    'did',
+    'does',
+    'either',
+    'ever',
+    'every',
+    'from',
+    'got',
+    'had',
+    'has',
+    'have',
+    'he',
+    'her',
+    'hers',
+    'him',
+    'his',
+    'how',
+    'however',
+    'i',
+    'if',
+    'into',
+    'it',
+    'its',
+    'just',
+    'least',
+    'like',
+    'likely',
+    'may',
+    'me',
+    'might',
+    'most',
+    'must',
+    'my',
+    'neither',
+    'no',
+    'nor',
+    'not',
+    'of',
+    'off',
+    'often',
+    'on',
+    'or',
+    'other',
+    'our',
+    'own',
+    'rather',
+    'said',
+    'say',
+    'says',
+    'she',
+    'should',
+    'since',
+    'so',
+    'some',
+    'than',
+    'that',
+    'the',
+    'their',
+    'them',
+    'then',
+    'there',
+    'these',
+    'they',
+    'this',
+    'tis',
+    'to',
+    'too',
+    'twas',
+    'us',
+    'wants',
+    'was',
+    'we',
+    'were',
+    'what',
+    'when',
+    'who',
+    'whom',
+    'why',
+    'will',
+    'would',
+    'yet',
+    'you',
+    'your'
+  ])
+
+  // add . as a separator, because otherwise "title": "Documenter.Anchors.add!"
+  // would not find anything if searching for "add!", only for the entire qualification
+  lunr.tokenizer.separator = /[\s\-\.]+/
+
+  // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names
+  lunr.trimmer = function (token) {
+    return token.update(function (s) {
+      return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '')
+    })
+  }
+
+  lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter')
+  lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer')
+
+  var index = lunr(function () {
+    this.ref('location')
+    this.field('title',{boost: 100})
+    this.field('text')
+    documenterSearchIndex['docs'].forEach(function(e) {
+        this.add(e)
+    }, this)
+  })
+  var store = {}
+
+  documenterSearchIndex['docs'].forEach(function(e) {
+      store[e.location] = {title: e.title, category: e.category, page: e.page}
+  })
+
+  $(function(){
+    searchresults = $('#documenter-search-results');
+    searchinfo = $('#documenter-search-info');
+    searchbox = $('#documenter-search-query');
+    searchform = $('.docs-search');
+    sidebar = $('.docs-sidebar');
+    function update_search(querystring) {
+      tokens = lunr.tokenizer(querystring)
+      results = index.query(function (q) {
+        tokens.forEach(function (t) {
+          q.term(t.toString(), {
+            fields: ["title"],
+            boost: 100,
+            usePipeline: true,
+            editDistance: 0,
+            wildcard: lunr.Query.wildcard.NONE
+          })
+          q.term(t.toString(), {
+            fields: ["title"],
+            boost: 10,
+            usePipeline: true,
+            editDistance: 2,
+            wildcard: lunr.Query.wildcard.NONE
+          })
+          q.term(t.toString(), {
+            fields: ["text"],
+            boost: 1,
+            usePipeline: true,
+            editDistance: 0,
+            wildcard: lunr.Query.wildcard.NONE
+          })
+        })
+      })
+      searchinfo.text("Number of results: " + results.length)
+      searchresults.empty()
+      results.forEach(function(result) {
+        data = store[result.ref]
+        link = $('<a class="docs-label">'+data.title+'</a>')
+        link.attr('href', documenterBaseURL+'/'+result.ref)
+        if (data.category != "page"){
+          cat = $('<span class="docs-category">('+data.category+', '+data.page+')</span>')
+        } else {
+          cat = $('<span class="docs-category">('+data.category+')</span>')
+        }
+        li = $('<li>').append(link).append(" ").append(cat)
+        searchresults.append(li)
+      })
+    }
+
+    function update_search_box() {
+      querystring = searchbox.val()
+      update_search(querystring)
+    }
+
+    searchbox.keyup(_.debounce(update_search_box, 250))
+    searchbox.change(update_search_box)
+
+    // Disable enter-key form submission for the searchbox on the search page
+    // and just re-run search rather than refresh the whole page.
+    searchform.keypress(
+      function(event){
+        if (event.which == '13') {
+          if (sidebar.hasClass('visible')) {
+            sidebar.removeClass('visible');
+          }
+          update_search_box();
+          event.preventDefault();
+        }
+      }
+    );
+
+    search_query_uri = parseUri(window.location).queryKey["q"]
+    if(search_query_uri !== undefined) {
+      search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20'))
+      searchbox.val(search_query)
+    }
+    update_search_box();
+  })
+})
+
+})
diff --git a/previews/PR41/assets/style.css b/previews/PR41/assets/style.css
new file mode 100644
index 0000000..07c73de
--- /dev/null
+++ b/previews/PR41/assets/style.css
@@ -0,0 +1,21 @@
+.mi, .mo, .mn {
+    color: #317293;
+  }
+  
+  a {
+    color: #3091d1;
+  }
+  
+  a:visited {
+    color: #3091d1;
+  }
+  
+  a:hover {
+    color: #ff5722;
+  }
+  
+  nav.toc .logo {
+    max-width: 256px;
+    max-height: 256px;
+  }
+  
\ No newline at end of file
diff --git a/previews/PR41/assets/themes/documenter-dark.css b/previews/PR41/assets/themes/documenter-dark.css
new file mode 100644
index 0000000..c94a294
--- /dev/null
+++ b/previews/PR41/assets/themes/documenter-dark.css
@@ -0,0 +1,7 @@
+@keyframes spinAround{from{transform:rotate(0deg)}to{transform:rotate(359deg)}}html.theme--documenter-dark .tabs,html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .breadcrumb,html.theme--documenter-dark .file,html.theme--documenter-dark .button,.is-unselectable,html.theme--documenter-dark .modal-close,html.theme--documenter-dark .delete{-webkit-touch-callout:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none}html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after,html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after{border:3px solid rgba(0,0,0,0);border-radius:2px;border-right:0;border-top:0;content:" 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+  Author: @ericwbailey
+  Maintainer: @ericwbailey
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!important}html.theme--documenter-dark .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#ecf0f1;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:#282f2f;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:transparent;color:#ecf0f1}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#232829;border-color:transparent;color:#ecf0f1}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#ecf0f1}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(40,47,47,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#1d2122;border-color:transparent;color:#ecf0f1}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#ecf0f1;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#dde4e6}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#ecf0f1;border-color:transparent;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#282f2f;border-color:#282f2f;color:#ecf0f1}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#ecf0f1;color:#ecf0f1}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#ecf0f1;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark 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.docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--documenter-dark .button.is-primary.is-outlined:focus,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-outlined.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#375a7f;border-color:#375a7f;color:#fff}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #375a7f #375a7f !important}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark 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a.navbar-item:hover{background-color:rgba(0,0,0,0);color:#dbdee0}html.theme--documenter-dark .navbar-dropdown a.navbar-item.is-active{background-color:rgba(0,0,0,0);color:#1abc9c}.navbar.is-spaced html.theme--documenter-dark .navbar-dropdown,html.theme--documenter-dark .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--documenter-dark .navbar-dropdown.is-right{left:auto;right:0}html.theme--documenter-dark .navbar-divider{display:block}html.theme--documenter-dark .navbar>.container .navbar-brand,html.theme--documenter-dark .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--documenter-dark .navbar>.container .navbar-menu,html.theme--documenter-dark .container>.navbar .navbar-menu{margin-right:-.75rem}html.theme--documenter-dark .navbar.is-fixed-bottom-desktop,html.theme--documenter-dark .navbar.is-fixed-top-desktop{left:0;position:fixed;right:0;z-index:30}html.theme--documenter-dark .navbar.is-fixed-bottom-desktop{bottom:0}html.theme--documenter-dark .navbar.is-fixed-bottom-desktop.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--documenter-dark .navbar.is-fixed-top-desktop{top:0}html.theme--documenter-dark html.has-navbar-fixed-top-desktop,html.theme--documenter-dark body.has-navbar-fixed-top-desktop{padding-top:4rem}html.theme--documenter-dark html.has-navbar-fixed-bottom-desktop,html.theme--documenter-dark body.has-navbar-fixed-bottom-desktop{padding-bottom:4rem}html.theme--documenter-dark html.has-spaced-navbar-fixed-top,html.theme--documenter-dark body.has-spaced-navbar-fixed-top{padding-top:6rem}html.theme--documenter-dark html.has-spaced-navbar-fixed-bottom,html.theme--documenter-dark body.has-spaced-navbar-fixed-bottom{padding-bottom:6rem}html.theme--documenter-dark a.navbar-item.is-active,html.theme--documenter-dark .navbar-link.is-active{color:#1abc9c}html.theme--documenter-dark a.navbar-item.is-active:not(:focus):not(:hover),html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--documenter-dark .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--documenter-dark .pagination{font-size:15px;margin:-.25rem}html.theme--documenter-dark .pagination.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.85em}html.theme--documenter-dark .pagination.is-medium{font-size:1.25rem}html.theme--documenter-dark .pagination.is-large{font-size:1.5rem}html.theme--documenter-dark 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.pagination-ellipsis{font-size:1em;justify-content:center;margin:.25rem;padding-left:.5em;padding-right:.5em;text-align:center}html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link{border-color:#5e6d6f;color:#1abc9c;min-width:2.25em}html.theme--documenter-dark .pagination-previous:hover,html.theme--documenter-dark .pagination-next:hover,html.theme--documenter-dark .pagination-link:hover{border-color:#8c9b9d;color:#1dd2af}html.theme--documenter-dark .pagination-previous:focus,html.theme--documenter-dark .pagination-next:focus,html.theme--documenter-dark .pagination-link:focus{border-color:#8c9b9d}html.theme--documenter-dark .pagination-previous:active,html.theme--documenter-dark .pagination-next:active,html.theme--documenter-dark .pagination-link:active{box-shadow:inset 0 1px 2px rgba(10,10,10,0.2)}html.theme--documenter-dark .pagination-previous[disabled],html.theme--documenter-dark 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.panel-block{align-items:center;color:#f2f2f2;display:flex;justify-content:flex-start;padding:0.5em 0.75em}html.theme--documenter-dark .panel-block input[type="checkbox"]{margin-right:0.75em}html.theme--documenter-dark .panel-block>.control{flex-grow:1;flex-shrink:1;width:100%}html.theme--documenter-dark .panel-block.is-wrapped{flex-wrap:wrap}html.theme--documenter-dark .panel-block.is-active{border-left-color:#1abc9c;color:#17a689}html.theme--documenter-dark .panel-block.is-active .panel-icon{color:#1abc9c}html.theme--documenter-dark a.panel-block,html.theme--documenter-dark label.panel-block{cursor:pointer}html.theme--documenter-dark a.panel-block:hover,html.theme--documenter-dark label.panel-block:hover{background-color:#282f2f}html.theme--documenter-dark .panel-icon{display:inline-block;font-size:14px;height:1em;line-height:1em;text-align:center;vertical-align:top;width:1em;color:#fff;margin-right:0.75em}html.theme--documenter-dark .panel-icon 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+  Theme: Default
+  Description: Original highlight.js style
+  Author: (c) Ivan Sagalaev <maniac@softwaremaniacs.org>
+  Maintainer: @highlightjs/core-team
+  Website: https://highlightjs.org/
+  License: see project LICENSE
+  Touched: 2021
+*/pre code.hljs{display:block;overflow-x:auto}code.hljs{padding:3px 5px}.hljs{background:#F0F0F0;color:#444}.hljs-comment{color:#888888}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#BC6060}.hljs-literal{color:#78A960}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#4d99bf}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}
diff --git a/previews/PR41/assets/themeswap.js b/previews/PR41/assets/themeswap.js
new file mode 100644
index 0000000..c58e993
--- /dev/null
+++ b/previews/PR41/assets/themeswap.js
@@ -0,0 +1,66 @@
+// Small function to quickly swap out themes. Gets put into the <head> tag..
+function set_theme_from_local_storage() {
+  // Intialize the theme to null, which means default
+  var theme = null;
+  // If the browser supports the localstorage and is not disabled then try to get the
+  // documenter theme
+  if(window.localStorage != null) {
+    // Get the user-picked theme from localStorage. May be `null`, which means the default
+    // theme.
+    theme =  window.localStorage.getItem("documenter-theme");
+  }
+  // Check if the browser supports user color preference
+  var darkPreference = false;
+  // Check if the users preference is for dark color scheme
+  if(window.matchMedia('(prefers-color-scheme: dark)').matches === true) {
+    darkPreference = true;
+  }
+  // Initialize a few variables for the loop:
+  //
+  //  - active: will contain the index of the theme that should be active. Note that there
+  //    is no guarantee that localStorage contains sane values. If `active` stays `null`
+  //    we either could not find the theme or it is the default (primary) theme anyway.
+  //    Either way, we then need to stick to the primary theme.
+  //
+  //  - disabled: style sheets that should be disabled (i.e. all the theme style sheets
+  //    that are not the currently active theme)
+  var active = null; var disabled = []; var darkTheme = null;
+  for (var i = 0; i < document.styleSheets.length; i++) {
+    var ss = document.styleSheets[i];
+    // The <link> tag of each style sheet is expected to have a data-theme-name attribute
+    // which must contain the name of the theme. The names in localStorage much match this.
+    var themename = ss.ownerNode.getAttribute("data-theme-name");
+    // attribute not set => non-theme stylesheet => ignore
+    if(themename === null) continue;
+    // To distinguish the default (primary) theme, it needs to have the data-theme-primary
+    // attribute set.
+    var isprimary = (ss.ownerNode.getAttribute("data-theme-primary") !== null);
+    // Check if the theme is primary dark theme
+    var isDarkTheme = (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null);
+    // If ss is for dark theme then set the value of darkTheme to the name of the theme
+    if(isDarkTheme) darkTheme = themename;
+    // If we find a matching theme (and it's not the default), we'll set active to non-null
+    if(themename === theme) active = i;
+    // Store the style sheets of inactive themes so that we could disable them
+    if(themename !== theme) disabled.push(ss);
+  }
+  if(active !== null) {
+    // If we did find an active theme, we'll (1) add the theme--$(theme) class to <html>
+    document.getElementsByTagName('html')[0].className = "theme--" + theme;
+    // and (2) disable all the other theme stylesheets
+    disabled.forEach(function(ss){
+      ss.disabled = true;
+    });
+  }
+  else if(darkTheme !== null && darkPreference === true) {
+    // If we did find an active theme, we'll (1) add the theme--$(theme) class to <html>
+    document.getElementsByTagName('html')[0].className = "theme--" + darkTheme;
+    // and (2) disable all the other theme stylesheets
+    disabled.forEach(function(ss){
+      if (ss.ownerNode.getAttribute("data-theme-name") !== darkTheme) {
+        ss.disabled = true;
+      }
+    });
+  }
+}
+set_theme_from_local_storage();
diff --git a/previews/PR41/assets/warner.js b/previews/PR41/assets/warner.js
new file mode 100644
index 0000000..5531c88
--- /dev/null
+++ b/previews/PR41/assets/warner.js
@@ -0,0 +1,49 @@
+function maybeAddWarning () {
+    // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE
+    // in siteinfo.js.
+    // If either of these are undefined something went horribly wrong, so we abort.
+    if (
+            window.DOCUMENTER_NEWEST === undefined ||
+            window.DOCUMENTER_CURRENT_VERSION === undefined ||
+            window.DOCUMENTER_STABLE === undefined
+       ) {
+        return
+    };
+
+    // Current version is not a version number, so we can't tell if it's the newest version. Abort.
+    if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) {
+        return
+    };
+
+    // Current version is newest version, so no need to add a warning.
+    if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) {
+        return
+    };
+
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+<!DOCTYPE html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>COPS · PDEOptimizationProblems</title><script data-outdated-warner src="../assets/warner.js"></script><link rel="canonical" href="https://tmigot.github.io/PDEOptimizationProblems/cops/"/><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script><link href="../assets/style.css" rel="stylesheet" type="text/css"/></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../"><img src="../assets/logo.png" alt="PDEOptimizationProblems logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../">PDEOptimizationProblems</a></span></div><form class="docs-search" action="../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li class="is-active"><a class="tocitem" href>COPS</a><ul class="internal"><li><a class="tocitem" href="#DCILDL"><span>DCILDL</span></a></li><li><a class="tocitem" href="#knitro"><span>knitro</span></a></li><li><a class="tocitem" href="#ipopt"><span>ipopt</span></a></li></ul></li><li><a class="tocitem" href="../tuto_rocket/">Rocket Control</a></li><li><a class="tocitem" href="../reference/">Reference</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>COPS</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>COPS</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/tmigot/PDEOptimizationProblems/blob/main/docs/src/cops.md#" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Simulations-on-COPS-3-test-set"><a class="docs-heading-anchor" href="#Simulations-on-COPS-3-test-set">Simulations on COPS 3 test set</a><a id="Simulations-on-COPS-3-test-set-1"></a><a class="docs-heading-anchor-permalink" href="#Simulations-on-COPS-3-test-set" title="Permalink"></a></h1><p>We run <a href="https://github.com/JuliaSmoothOptimizers/DCISolver.jl">DCISolver.jl</a> and <a href="https://github.com/JuliaSmoothOptimizers/DCISolver.jl">NLPModelsIpopt.jl</a> and <a href="https://github.com/JuliaSmoothOptimizers/NLPModelsKnitro.jl">NLPModelsKnitro.jl</a> on an infinite-dimensional implementation of test problems from <a href="https://www.mcs.anl.gov/~more/cops/">COPS 3.0</a> test set.</p><h2 id="DCILDL"><a class="docs-heading-anchor" href="#DCILDL">DCILDL</a><a id="DCILDL-1"></a><a class="docs-heading-anchor-permalink" href="#DCILDL" title="Permalink"></a></h2><table><tr><th style="text-align: right">name</th><th style="text-align: right">nvar</th><th style="text-align: right">ncon</th><th style="text-align: right">status</th><th style="text-align: right">objective</th><th style="text-align: right">opt_val</th><th style="text-align: right">time (s)</th><th style="text-align: right">#f</th><th style="text-align: right">#c</th><th style="text-align: right">dual_feas</th><th style="text-align: right">feas</th></tr><tr><td style="text-align: right">Isometrization of α-pinene</td><td style="text-align: right">505</td><td style="text-align: right">500</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.99e+01</td><td style="text-align: right">8.49e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">2.84e+01</td></tr><tr><td style="text-align: right">Isometrization of α-pinene</td><td style="text-align: right">1005</td><td style="text-align: right">1000</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.99e+01</td><td style="text-align: right">4.05e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">2.84e+01</td></tr><tr><td style="text-align: right">Isometrization of α-pinene</td><td style="text-align: right">2005</td><td style="text-align: right">2000</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.99e+01</td><td style="text-align: right">4.42e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">2.84e+01</td></tr><tr><td style="text-align: right">Journal Bearing</td><td style="text-align: right">2600</td><td style="text-align: right">0</td><td style="text-align: right">exception</td><td style="text-align: right">Inf</td><td style="text-align: right">-1.55e-01</td><td style="text-align: right">Inf</td><td style="text-align: right">0</td><td style="text-align: right">0</td><td style="text-align: right">Inf</td><td style="text-align: right">Inf</td></tr><tr><td style="text-align: right">Journal Bearing</td><td style="text-align: right">5775</td><td style="text-align: right">0</td><td style="text-align: right">exception</td><td style="text-align: right">Inf</td><td style="text-align: right">-1.55e-01</td><td style="text-align: right">Inf</td><td style="text-align: right">0</td><td style="text-align: right">0</td><td style="text-align: right">Inf</td><td style="text-align: right">Inf</td></tr><tr><td style="text-align: right">Journal Bearing</td><td style="text-align: right">10200</td><td style="text-align: right">0</td><td style="text-align: right">exception</td><td style="text-align: right">Inf</td><td style="text-align: right">-1.55e-01</td><td style="text-align: right">Inf</td><td style="text-align: right">0</td><td style="text-align: right">0</td><td style="text-align: right">Inf</td><td style="text-align: right">Inf</td></tr><tr><td style="text-align: right">Catalyst Mixing</td><td style="text-align: right">602</td><td style="text-align: right">402</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">-4.81e-02</td><td style="text-align: right">9.96e+01</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">1.41e-01</td><td style="text-align: right">2.50e-01</td></tr><tr><td style="text-align: right">Catalyst Mixing</td><td style="text-align: right">1202</td><td style="text-align: right">802</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">-4.81e-02</td><td style="text-align: right">3.94e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">9.98e-02</td><td style="text-align: right">2.50e-01</td></tr><tr><td style="text-align: right">Catalyst Mixing</td><td style="text-align: right">2402</td><td style="text-align: right">1602</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">-4.81e-02</td><td style="text-align: right">1.07e+03</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">7.07e-02</td><td style="text-align: right">2.50e-01</td></tr><tr><td style="text-align: right">Flow in a Channel</td><td style="text-align: right">800</td><td style="text-align: right">800</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.00e+00</td><td style="text-align: right">5.14e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">2.20e-01</td></tr><tr><td style="text-align: right">Flow in a Channel</td><td style="text-align: right">1600</td><td style="text-align: right">1600</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.00e+00</td><td style="text-align: right">2.57e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">2.20e-01</td></tr><tr><td style="text-align: right">Flow in a Channel</td><td style="text-align: right">3200</td><td style="text-align: right">3200</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.00e+00</td><td style="text-align: right">2.78e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">2.20e-01</td></tr><tr><td style="text-align: right">Transition States for the Dirichlet Problem</td><td style="text-align: right">9</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.94e-06</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Transition States for the Dirichlet Problem</td><td style="text-align: right">19</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.71e-02</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Transition States for the Dirichlet Problem</td><td style="text-align: right">39</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">3.29e-02</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Catalytic Cracking of Gas Oil</td><td style="text-align: right">205</td><td style="text-align: right">202</td><td style="text-align: right">max_time</td><td style="text-align: right">8.21e-02</td><td style="text-align: right">5.24e-03</td><td style="text-align: right">6.83e+01</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">4.19e-02</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Catalytic Cracking of Gas Oil</td><td style="text-align: right">405</td><td style="text-align: right">402</td><td style="text-align: right">max_time</td><td style="text-align: right">8.11e-02</td><td style="text-align: right">5.24e-03</td><td style="text-align: right">1.11e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">2.97e-02</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Catalytic Cracking of Gas Oil</td><td style="text-align: right">805</td><td style="text-align: right">802</td><td style="text-align: right">max_time</td><td style="text-align: right">8.11e-02</td><td style="text-align: right">5.24e-03</td><td style="text-align: right">2.21e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">2.10e-02</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Hang Glider</td><td style="text-align: right">698</td><td style="text-align: right">498</td><td style="text-align: right">max_time</td><td style="text-align: right">-9.50e+02</td><td style="text-align: right">1.25e+03</td><td style="text-align: right">4.51e+03</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">4.75e-15</td><td style="text-align: right">8.79e+01</td></tr><tr><td style="text-align: right">Hang Glider</td><td style="text-align: right">1398</td><td style="text-align: right">998</td><td style="text-align: right">max_time</td><td style="text-align: right">-9.50e+02</td><td style="text-align: right">1.25e+03</td><td style="text-align: right">8.86e+03</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">6.76e-15</td><td style="text-align: right">6.44e+01</td></tr><tr><td style="text-align: right">Hang Glider</td><td style="text-align: right">2798</td><td style="text-align: right">1998</td><td style="text-align: right">max_time</td><td style="text-align: right">-9.50e+02</td><td style="text-align: right">1.25e+03</td><td style="text-align: right">1.77e+04</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">5.05e-09</td><td style="text-align: right">4.66e+01</td></tr><tr><td style="text-align: right">Transition States for the Henon Problem</td><td style="text-align: right">9</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">7.22e+00</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Transition States for the Henon Problem</td><td style="text-align: right">19</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">7.52e+01</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Transition States for the Henon Problem</td><td style="text-align: right">39</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.26e+02</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Transition States for the Lane-Emden Problem</td><td style="text-align: right">9</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">8.49e+00</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Transition States for the Lane-Emden Problem</td><td style="text-align: right">19</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">9.11e+00</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Transition States for the Lane-Emden Problem</td><td style="text-align: right">39</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">9.28e+00</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Methanol to Hydrocarbons</td><td style="text-align: right">308</td><td style="text-align: right">303</td><td style="text-align: right">exception</td><td style="text-align: right">Inf</td><td style="text-align: right">9.02e-03</td><td style="text-align: right">Inf</td><td style="text-align: right">0</td><td style="text-align: right">0</td><td style="text-align: right">Inf</td><td style="text-align: right">Inf</td></tr><tr><td style="text-align: right">Methanol to Hydrocarbons</td><td style="text-align: right">608</td><td style="text-align: right">603</td><td style="text-align: right">exception</td><td style="text-align: right">Inf</td><td style="text-align: right">9.02e-03</td><td style="text-align: right">Inf</td><td style="text-align: right">0</td><td style="text-align: right">0</td><td style="text-align: right">Inf</td><td style="text-align: right">Inf</td></tr><tr><td style="text-align: right">Methanol to Hydrocarbons</td><td style="text-align: right">1208</td><td style="text-align: right">1203</td><td style="text-align: right">exception</td><td style="text-align: right">Inf</td><td style="text-align: right">9.02e-03</td><td style="text-align: right">Inf</td><td style="text-align: right">0</td><td style="text-align: right">0</td><td style="text-align: right">Inf</td><td style="text-align: right">Inf</td></tr><tr><td style="text-align: right">Minimal Surface with Obstacle</td><td style="text-align: right">5002</td><td style="text-align: right">2401</td><td style="text-align: right">max_time</td><td style="text-align: right">2.33e+00</td><td style="text-align: right">2.51e+00</td><td style="text-align: right">1.94e+01</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">6.85e-02</td><td style="text-align: right">7.34e-03</td></tr><tr><td style="text-align: right">Minimal Surface with Obstacle</td><td style="text-align: right">11252</td><td style="text-align: right">5476</td><td style="text-align: right">max_time</td><td style="text-align: right">2.32e+00</td><td style="text-align: right">2.51e+00</td><td style="text-align: right">1.59e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">5.29e-02</td><td style="text-align: right">5.08e-03</td></tr><tr><td style="text-align: right">Minimal Surface with Obstacle</td><td style="text-align: right">20002</td><td style="text-align: right">9801</td><td style="text-align: right">max_time</td><td style="text-align: right">2.33e+00</td><td style="text-align: right">2.51e+00</td><td style="text-align: right">2.33e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">4.44e-02</td><td style="text-align: right">3.84e-03</td></tr><tr><td style="text-align: right">Robot Arm</td><td style="text-align: right">1200</td><td style="text-align: right">597</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">9.14e+00</td><td style="text-align: right">3.74e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">2.01e+04</td></tr><tr><td style="text-align: right">Robot Arm</td><td style="text-align: right">2400</td><td style="text-align: right">1197</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">9.14e+00</td><td style="text-align: right">3.87e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">4.02e+04</td></tr><tr><td style="text-align: right">Robot Arm</td><td style="text-align: right">4800</td><td style="text-align: right">2397</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">9.14e+00</td><td style="text-align: right">4.08e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">8.04e+04</td></tr><tr><td style="text-align: right">Goddard Rocket</td><td style="text-align: right">2400</td><td style="text-align: right">1600</td><td style="text-align: right">max_time</td><td style="text-align: right">-1.00e+00</td><td style="text-align: right">1.01e+00</td><td style="text-align: right">4.83e+04</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">1.85e-02</td><td style="text-align: right">2.64e-01</td></tr><tr><td style="text-align: right">Goddard Rocket</td><td style="text-align: right">4800</td><td style="text-align: right">3200</td><td style="text-align: right">max_time</td><td style="text-align: right">-1.00e+00</td><td style="text-align: right">1.01e+00</td><td style="text-align: right">5.78e+04</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">1.32e-02</td><td style="text-align: right">1.90e-01</td></tr><tr><td style="text-align: right">Goddard Rocket</td><td style="text-align: right">9600</td><td style="text-align: right">6400</td><td style="text-align: right">max_time</td><td style="text-align: right">-1.00e+00</td><td style="text-align: right">1.01e+00</td><td style="text-align: right">1.23e+05</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">9.39e-03</td><td style="text-align: right">1.69e-01</td></tr><tr><td style="text-align: right">Particle Steering</td><td style="text-align: right">800</td><td style="text-align: right">400</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">5.55e-01</td><td style="text-align: right">5.91e+01</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.35e+01</td></tr><tr><td style="text-align: right">Particle Steering</td><td style="text-align: right">1600</td><td style="text-align: right">800</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">5.55e-01</td><td style="text-align: right">1.80e+02</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">9.56e+00</td></tr><tr><td style="text-align: right">Particle Steering</td><td style="text-align: right">3200</td><td style="text-align: right">1600</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">5.55e-01</td><td style="text-align: right">6.38e+02</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">6.79e+00</td></tr><tr><td style="text-align: right">Elastic-Plastic Torsion</td><td style="text-align: right">7802</td><td style="text-align: right">7802</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">-4.18e-01</td><td style="text-align: right">5.58e+01</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">5.72e-02</td><td style="text-align: right">9.93e-03</td></tr><tr><td style="text-align: right">Elastic-Plastic Torsion</td><td style="text-align: right">17327</td><td style="text-align: right">17327</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">-4.18e-01</td><td style="text-align: right">2.22e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">3.82e-02</td><td style="text-align: right">6.64e-03</td></tr><tr><td style="text-align: right">Elastic-Plastic Torsion</td><td style="text-align: right">30602</td><td style="text-align: right">30602</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">-4.18e-01</td><td style="text-align: right">2.71e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">2.87e-02</td><td style="text-align: right">4.98e-03</td></tr></table><h2 id="knitro"><a class="docs-heading-anchor" href="#knitro">knitro</a><a id="knitro-1"></a><a class="docs-heading-anchor-permalink" href="#knitro" title="Permalink"></a></h2><table><tr><th style="text-align: right">name</th><th style="text-align: right">nvar</th><th style="text-align: right">ncon</th><th style="text-align: right">status</th><th style="text-align: right">objective</th><th style="text-align: right">opt_val</th><th style="text-align: right">time (s)</th><th style="text-align: right">#f</th><th style="text-align: right">#c</th><th style="text-align: right">dual_feas</th><th style="text-align: right">feas</th></tr><tr><td style="text-align: right">Isometrization of α-pinene</td><td style="text-align: right">505</td><td style="text-align: right">500</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.99e+01</td><td style="text-align: right">4.33e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">5.00e+01</td></tr><tr><td style="text-align: right">Isometrization of α-pinene</td><td style="text-align: right">1005</td><td style="text-align: right">1000</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.99e+01</td><td style="text-align: right">1.10e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">5.00e+01</td></tr><tr><td style="text-align: right">Isometrization of α-pinene</td><td style="text-align: right">2005</td><td style="text-align: right">2000</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.99e+01</td><td style="text-align: right">1.26e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">5.00e+01</td></tr><tr><td style="text-align: right">Journal Bearing</td><td style="text-align: right">2600</td><td style="text-align: right">0</td><td style="text-align: right">max_time</td><td style="text-align: right">1.20e+01</td><td style="text-align: right">-1.55e-01</td><td style="text-align: right">9.39e+00</td><td style="text-align: right">1</td><td style="text-align: right">0</td><td style="text-align: right">5.88e-01</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Journal Bearing</td><td style="text-align: right">5775</td><td style="text-align: right">0</td><td style="text-align: right">max_time</td><td style="text-align: right">5.06e+00</td><td style="text-align: right">-1.55e-01</td><td style="text-align: right">5.31e+00</td><td style="text-align: right">2</td><td style="text-align: right">0</td><td style="text-align: right">2.31e-01</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Journal Bearing</td><td style="text-align: right">10200</td><td style="text-align: right">0</td><td style="text-align: right">max_time</td><td style="text-align: right">-1.05e+00</td><td style="text-align: right">-1.55e-01</td><td style="text-align: right">1.09e+00</td><td style="text-align: right">5</td><td style="text-align: right">0</td><td style="text-align: right">3.17e-04</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Catalyst Mixing</td><td style="text-align: right">602</td><td style="text-align: right">402</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">-4.81e-02</td><td style="text-align: right">2.82e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">1.00e-02</td><td style="text-align: right">2.49e-01</td></tr><tr><td style="text-align: right">Catalyst Mixing</td><td style="text-align: right">1202</td><td style="text-align: right">802</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">-4.81e-02</td><td style="text-align: right">2.56e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">5.00e-03</td><td style="text-align: right">2.49e-01</td></tr><tr><td style="text-align: right">Catalyst Mixing</td><td style="text-align: right">2402</td><td style="text-align: right">1602</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">-4.81e-02</td><td style="text-align: right">3.60e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">2.50e-03</td><td style="text-align: right">2.50e-01</td></tr><tr><td style="text-align: right">Flow in a Channel</td><td style="text-align: right">800</td><td style="text-align: right">800</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.00e+00</td><td style="text-align: right">5.12e+01</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.99e-13</td></tr><tr><td style="text-align: right">Flow in a Channel</td><td style="text-align: right">1600</td><td style="text-align: right">1600</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.00e+00</td><td style="text-align: right">1.58e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">4.44e-16</td></tr><tr><td style="text-align: right">Flow in a Channel</td><td style="text-align: right">3200</td><td style="text-align: right">3200</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.00e+00</td><td style="text-align: right">1.55e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">6.66e-16</td></tr><tr><td style="text-align: right">Transition States for the Dirichlet Problem</td><td style="text-align: right">9</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.94e-06</td><td style="text-align: right">5.16e-02</td><td style="text-align: right">1</td><td style="text-align: right">0</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Transition States for the Dirichlet Problem</td><td style="text-align: right">19</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.71e-02</td><td style="text-align: right">1.99e-01</td><td style="text-align: right">1</td><td style="text-align: right">0</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Transition States for the Dirichlet Problem</td><td style="text-align: right">39</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">3.29e-02</td><td style="text-align: right">4.02e-02</td><td style="text-align: right">1</td><td style="text-align: right">0</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Catalytic Cracking of Gas Oil</td><td style="text-align: right">205</td><td style="text-align: right">202</td><td style="text-align: right">max_time</td><td style="text-align: right">7.94e-02</td><td style="text-align: right">5.24e-03</td><td style="text-align: right">5.73e+01</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">7.01e-03</td><td style="text-align: right">4.86e-07</td></tr><tr><td style="text-align: right">Catalytic Cracking of Gas Oil</td><td style="text-align: right">405</td><td style="text-align: right">402</td><td style="text-align: right">max_time</td><td style="text-align: right">7.93e-02</td><td style="text-align: right">5.24e-03</td><td style="text-align: right">1.45e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">5.73e-03</td><td style="text-align: right">3.20e-07</td></tr><tr><td style="text-align: right">Catalytic Cracking of Gas Oil</td><td style="text-align: right">805</td><td style="text-align: right">802</td><td style="text-align: right">max_time</td><td style="text-align: right">4.65e-02</td><td style="text-align: right">5.24e-03</td><td style="text-align: right">2.88e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">3.14e-03</td><td style="text-align: right">7.89e-05</td></tr><tr><td style="text-align: right">Hang Glider</td><td style="text-align: right">698</td><td style="text-align: right">498</td><td style="text-align: right">max_time</td><td style="text-align: right">-9.50e+02</td><td style="text-align: right">1.25e+03</td><td style="text-align: right">2.77e+01</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">4.44e-16</td><td style="text-align: right">9.73e+00</td></tr><tr><td style="text-align: right">Hang Glider</td><td style="text-align: right">1398</td><td style="text-align: right">998</td><td style="text-align: right">max_time</td><td style="text-align: right">-9.50e+02</td><td style="text-align: right">1.25e+03</td><td style="text-align: right">2.74e+01</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">6.66e-16</td><td style="text-align: right">4.86e+00</td></tr><tr><td style="text-align: right">Hang Glider</td><td style="text-align: right">2798</td><td style="text-align: right">1998</td><td style="text-align: right">max_time</td><td style="text-align: right">-9.50e+02</td><td style="text-align: right">1.25e+03</td><td style="text-align: right">2.77e+01</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">6.66e-16</td><td style="text-align: right">2.43e+00</td></tr><tr><td style="text-align: right">Transition States for the Henon Problem</td><td style="text-align: right">9</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">7.22e+00</td><td style="text-align: right">2.82e-02</td><td style="text-align: right">1</td><td style="text-align: right">0</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Transition States for the Henon Problem</td><td style="text-align: right">19</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">7.52e+01</td><td style="text-align: right">2.74e-02</td><td style="text-align: right">1</td><td style="text-align: right">0</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Transition States for the Henon Problem</td><td style="text-align: right">39</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.26e+02</td><td style="text-align: right">5.00e-02</td><td style="text-align: right">1</td><td style="text-align: right">0</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Transition States for the Lane-Emden Problem</td><td style="text-align: right">9</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">8.49e+00</td><td style="text-align: right">2.56e-02</td><td style="text-align: right">1</td><td style="text-align: right">0</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Transition States for the Lane-Emden Problem</td><td style="text-align: right">19</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">9.11e+00</td><td style="text-align: right">4.14e-02</td><td style="text-align: right">1</td><td style="text-align: right">0</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Transition States for the Lane-Emden Problem</td><td style="text-align: right">39</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">9.28e+00</td><td style="text-align: right">3.79e-02</td><td style="text-align: right">1</td><td style="text-align: right">0</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Methanol to Hydrocarbons</td><td style="text-align: right">308</td><td style="text-align: right">303</td><td style="text-align: right">exception</td><td style="text-align: right">2.33e-01</td><td style="text-align: right">9.02e-03</td><td style="text-align: right">6.73e-01</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">1.80e+308</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Methanol to Hydrocarbons</td><td style="text-align: right">608</td><td style="text-align: right">603</td><td style="text-align: right">exception</td><td style="text-align: right">2.33e-01</td><td style="text-align: right">9.02e-03</td><td style="text-align: right">5.03e-01</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">1.80e+308</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Methanol to Hydrocarbons</td><td style="text-align: right">1208</td><td style="text-align: right">1203</td><td style="text-align: right">exception</td><td style="text-align: right">2.33e-01</td><td style="text-align: right">9.02e-03</td><td style="text-align: right">6.91e-01</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">1.80e+308</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Minimal Surface with Obstacle</td><td style="text-align: right">5002</td><td style="text-align: right">2401</td><td style="text-align: right">max_time</td><td style="text-align: right">5.78e+00</td><td style="text-align: right">2.51e+00</td><td style="text-align: right">1.86e+01</td><td style="text-align: right">3</td><td style="text-align: right">3</td><td style="text-align: right">5.09e-02</td><td style="text-align: right">4.30e-04</td></tr><tr><td style="text-align: right">Minimal Surface with Obstacle</td><td style="text-align: right">11252</td><td style="text-align: right">5476</td><td style="text-align: right">max_time</td><td style="text-align: right">6.40e+00</td><td style="text-align: right">2.51e+00</td><td style="text-align: right">1.70e+00</td><td style="text-align: right">3</td><td style="text-align: right">3</td><td style="text-align: right">3.33e-02</td><td style="text-align: right">1.85e-04</td></tr><tr><td style="text-align: right">Minimal Surface with Obstacle</td><td style="text-align: right">20002</td><td style="text-align: right">9801</td><td style="text-align: right">max_time</td><td style="text-align: right">8.47e+00</td><td style="text-align: right">2.51e+00</td><td style="text-align: right">2.43e+00</td><td style="text-align: right">3</td><td style="text-align: right">3</td><td style="text-align: right">2.65e-02</td><td style="text-align: right">1.23e-04</td></tr><tr><td style="text-align: right">Robot Arm</td><td style="text-align: right">1200</td><td style="text-align: right">597</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">9.14e+00</td><td style="text-align: right">2.04e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">8.31e+03</td></tr><tr><td style="text-align: right">Robot Arm</td><td style="text-align: right">2400</td><td style="text-align: right">1197</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">9.14e+00</td><td style="text-align: right">1.79e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.66e+04</td></tr><tr><td style="text-align: right">Robot Arm</td><td style="text-align: right">4800</td><td style="text-align: right">2397</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">9.14e+00</td><td style="text-align: right">2.33e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">3.32e+04</td></tr><tr><td style="text-align: right">Goddard Rocket</td><td style="text-align: right">2400</td><td style="text-align: right">1600</td><td style="text-align: right">max_time</td><td style="text-align: right">-1.00e+00</td><td style="text-align: right">1.01e+00</td><td style="text-align: right">3.13e+00</td><td style="text-align: right">3</td><td style="text-align: right">3</td><td style="text-align: right">2.50e-03</td><td style="text-align: right">4.61e-02</td></tr><tr><td style="text-align: right">Goddard Rocket</td><td style="text-align: right">4800</td><td style="text-align: right">3200</td><td style="text-align: right">max_time</td><td style="text-align: right">-1.00e+00</td><td style="text-align: right">1.01e+00</td><td style="text-align: right">3.16e+00</td><td style="text-align: right">3</td><td style="text-align: right">3</td><td style="text-align: right">1.25e-03</td><td style="text-align: right">2.30e-02</td></tr><tr><td style="text-align: right">Goddard Rocket</td><td style="text-align: right">9600</td><td style="text-align: right">6400</td><td style="text-align: right">max_time</td><td style="text-align: right">-1.00e+00</td><td style="text-align: right">1.01e+00</td><td style="text-align: right">3.36e+00</td><td style="text-align: right">3</td><td style="text-align: right">3</td><td style="text-align: right">6.25e-04</td><td style="text-align: right">1.15e-02</td></tr><tr><td style="text-align: right">Particle Steering</td><td style="text-align: right">800</td><td style="text-align: right">400</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">5.55e-01</td><td style="text-align: right">1.80e+01</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">7.62e-12</td></tr><tr><td style="text-align: right">Particle Steering</td><td style="text-align: right">1600</td><td style="text-align: right">800</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">5.55e-01</td><td style="text-align: right">3.54e-01</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.66e-11</td></tr><tr><td style="text-align: right">Particle Steering</td><td style="text-align: right">3200</td><td style="text-align: right">1600</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">5.55e-01</td><td style="text-align: right">5.49e-01</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">2.86e-11</td></tr><tr><td style="text-align: right">Elastic-Plastic Torsion</td><td style="text-align: right">7802</td><td style="text-align: right">7802</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">-4.18e-01</td><td style="text-align: right">1.93e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">8.06e-04</td><td style="text-align: right">5.92e-04</td></tr><tr><td style="text-align: right">Elastic-Plastic Torsion</td><td style="text-align: right">17327</td><td style="text-align: right">17327</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">-4.18e-01</td><td style="text-align: right">1.19e+01</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">3.60e-04</td><td style="text-align: right">2.64e-04</td></tr><tr><td style="text-align: right">Elastic-Plastic Torsion</td><td style="text-align: right">30602</td><td style="text-align: right">30602</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">-4.18e-01</td><td style="text-align: right">2.72e+01</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">2.14e-04</td><td style="text-align: right">1.49e-04</td></tr></table><h2 id="ipopt"><a class="docs-heading-anchor" href="#ipopt">ipopt</a><a id="ipopt-1"></a><a class="docs-heading-anchor-permalink" href="#ipopt" title="Permalink"></a></h2><table><tr><th style="text-align: right">name</th><th style="text-align: right">nvar</th><th style="text-align: right">ncon</th><th style="text-align: right">status</th><th style="text-align: right">objective</th><th style="text-align: right">opt_val</th><th style="text-align: right">time (s)</th><th style="text-align: right">#f</th><th style="text-align: right">#c</th><th style="text-align: right">dual_feas</th><th style="text-align: right">feas</th></tr><tr><td style="text-align: right">Isometrization of α-pinene</td><td style="text-align: right">505</td><td style="text-align: right">500</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.99e+01</td><td style="text-align: right">1.67e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">5.00e+01</td></tr><tr><td style="text-align: right">Isometrization of α-pinene</td><td style="text-align: right">1005</td><td style="text-align: right">1000</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.99e+01</td><td style="text-align: right">1.83e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">5.00e+01</td></tr><tr><td style="text-align: right">Isometrization of α-pinene</td><td style="text-align: right">2005</td><td style="text-align: right">2000</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.99e+01</td><td style="text-align: right">2.02e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">5.00e+01</td></tr><tr><td style="text-align: right">Journal Bearing</td><td style="text-align: right">2600</td><td style="text-align: right">0</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">-1.55e-01</td><td style="text-align: right">1.06e+00</td><td style="text-align: right">9</td><td style="text-align: right">0</td><td style="text-align: right">2.19e-05</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Journal Bearing</td><td style="text-align: right">5775</td><td style="text-align: right">0</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">-1.55e-01</td><td style="text-align: right">1.08e+00</td><td style="text-align: right">4</td><td style="text-align: right">0</td><td style="text-align: right">5.14e-02</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Journal Bearing</td><td style="text-align: right">10200</td><td style="text-align: right">0</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">-1.55e-01</td><td style="text-align: right">1.07e+00</td><td style="text-align: right">3</td><td style="text-align: right">0</td><td style="text-align: right">1.74e-01</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Catalyst Mixing</td><td style="text-align: right">602</td><td style="text-align: right">402</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">-4.81e-02</td><td style="text-align: right">2.58e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">1.00e-02</td><td style="text-align: right">2.50e-01</td></tr><tr><td style="text-align: right">Catalyst Mixing</td><td style="text-align: right">1202</td><td style="text-align: right">802</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">-4.81e-02</td><td style="text-align: right">2.53e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">5.00e-03</td><td style="text-align: right">2.50e-01</td></tr><tr><td style="text-align: right">Catalyst Mixing</td><td style="text-align: right">2402</td><td style="text-align: right">1602</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">-4.81e-02</td><td style="text-align: right">5.93e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">2.50e-03</td><td style="text-align: right">2.50e-01</td></tr><tr><td style="text-align: right">Flow in a Channel</td><td style="text-align: right">800</td><td style="text-align: right">800</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.00e+00</td><td style="text-align: right">2.68e+01</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">2.00e-02</td><td style="text-align: right">3.32e-08</td></tr><tr><td style="text-align: right">Flow in a Channel</td><td style="text-align: right">1600</td><td style="text-align: right">1600</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.00e+00</td><td style="text-align: right">1.52e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">2.00e-02</td><td style="text-align: right">6.64e-08</td></tr><tr><td style="text-align: right">Flow in a Channel</td><td style="text-align: right">3200</td><td style="text-align: right">3200</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.00e+00</td><td style="text-align: right">1.15e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">2.00e-02</td><td style="text-align: right">1.33e-07</td></tr><tr><td style="text-align: right">Transition States for the Dirichlet Problem</td><td style="text-align: right">9</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.94e-06</td><td style="text-align: right">4.90e-02</td><td style="text-align: right">1</td><td style="text-align: right">0</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Transition States for the Dirichlet Problem</td><td style="text-align: right">19</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.71e-02</td><td style="text-align: right">1.48e-01</td><td style="text-align: right">1</td><td style="text-align: right">0</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Transition States for the Dirichlet Problem</td><td style="text-align: right">39</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">3.29e-02</td><td style="text-align: right">4.40e-02</td><td style="text-align: right">1</td><td style="text-align: right">0</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Catalytic Cracking of Gas Oil</td><td style="text-align: right">205</td><td style="text-align: right">202</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">5.24e-03</td><td style="text-align: right">2.90e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">1.03e-02</td><td style="text-align: right">5.89e-06</td></tr><tr><td style="text-align: right">Catalytic Cracking of Gas Oil</td><td style="text-align: right">405</td><td style="text-align: right">402</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">5.24e-03</td><td style="text-align: right">1.42e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">1.47e-02</td><td style="text-align: right">3.88e-06</td></tr><tr><td style="text-align: right">Catalytic Cracking of Gas Oil</td><td style="text-align: right">805</td><td style="text-align: right">802</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">5.24e-03</td><td style="text-align: right">1.88e+00</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">3.79e-02</td><td style="text-align: right">1.84e-06</td></tr><tr><td style="text-align: right">Hang Glider</td><td style="text-align: right">698</td><td style="text-align: right">498</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.25e+03</td><td style="text-align: right">3.71e+01</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">1.00e+00</td><td style="text-align: right">9.73e+00</td></tr><tr><td style="text-align: right">Hang Glider</td><td style="text-align: right">1398</td><td style="text-align: right">998</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.25e+03</td><td style="text-align: right">3.77e+01</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">1.00e+00</td><td style="text-align: right">4.86e+00</td></tr><tr><td style="text-align: right">Hang Glider</td><td style="text-align: right">2798</td><td style="text-align: right">1998</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.25e+03</td><td style="text-align: right">3.86e+01</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">1.00e+00</td><td style="text-align: right">2.43e+00</td></tr><tr><td style="text-align: right">Transition States for the Henon Problem</td><td style="text-align: right">9</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">7.22e+00</td><td style="text-align: right">3.60e-02</td><td style="text-align: right">1</td><td style="text-align: right">0</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Transition States for the Henon Problem</td><td style="text-align: right">19</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">7.52e+01</td><td style="text-align: right">4.00e-02</td><td style="text-align: right">1</td><td style="text-align: right">0</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Transition States for the Henon Problem</td><td style="text-align: right">39</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.26e+02</td><td style="text-align: right">1.36e-01</td><td style="text-align: right">1</td><td style="text-align: right">0</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Transition States for the Lane-Emden Problem</td><td style="text-align: right">9</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">8.49e+00</td><td style="text-align: right">3.80e-02</td><td style="text-align: right">1</td><td style="text-align: right">0</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Transition States for the Lane-Emden Problem</td><td style="text-align: right">19</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">9.11e+00</td><td style="text-align: right">4.00e-02</td><td style="text-align: right">1</td><td style="text-align: right">0</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Transition States for the Lane-Emden Problem</td><td style="text-align: right">39</td><td style="text-align: right">0</td><td style="text-align: right">first_order</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">9.28e+00</td><td style="text-align: right">3.90e-02</td><td style="text-align: right">1</td><td style="text-align: right">0</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">0.00e+00</td></tr><tr><td style="text-align: right">Methanol to Hydrocarbons</td><td style="text-align: right">308</td><td style="text-align: right">303</td><td style="text-align: right">unknown</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">9.02e-03</td><td style="text-align: right">1.67e+01</td><td style="text-align: right">0</td><td style="text-align: right">1</td><td style="text-align: right">Inf</td><td style="text-align: right">Inf</td></tr><tr><td style="text-align: right">Methanol to Hydrocarbons</td><td style="text-align: right">608</td><td style="text-align: right">603</td><td style="text-align: right">unknown</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">9.02e-03</td><td style="text-align: right">1.20e+00</td><td style="text-align: right">0</td><td style="text-align: right">1</td><td style="text-align: right">Inf</td><td style="text-align: right">Inf</td></tr><tr><td style="text-align: right">Methanol to Hydrocarbons</td><td style="text-align: right">1208</td><td style="text-align: right">1203</td><td style="text-align: right">unknown</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">9.02e-03</td><td style="text-align: right">1.03e+01</td><td style="text-align: right">0</td><td style="text-align: right">1</td><td style="text-align: right">Inf</td><td style="text-align: right">Inf</td></tr><tr><td style="text-align: right">Minimal Surface with Obstacle</td><td style="text-align: right">5002</td><td style="text-align: right">2401</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">2.51e+00</td><td style="text-align: right">1.29e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">1.00e+00</td><td style="text-align: right">3.84e-04</td></tr><tr><td style="text-align: right">Minimal Surface with Obstacle</td><td style="text-align: right">11252</td><td style="text-align: right">5476</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">2.51e+00</td><td style="text-align: right">1.14e+01</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">1.00e+00</td><td style="text-align: right">1.74e-04</td></tr><tr><td style="text-align: right">Minimal Surface with Obstacle</td><td style="text-align: right">20002</td><td style="text-align: right">9801</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">2.51e+00</td><td style="text-align: right">4.18e+01</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">1.00e+00</td><td style="text-align: right">9.85e-05</td></tr><tr><td style="text-align: right">Robot Arm</td><td style="text-align: right">1200</td><td style="text-align: right">597</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">9.14e+00</td><td style="text-align: right">2.07e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.41e+04</td></tr><tr><td style="text-align: right">Robot Arm</td><td style="text-align: right">2400</td><td style="text-align: right">1197</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">9.14e+00</td><td style="text-align: right">2.08e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">2.83e+04</td></tr><tr><td style="text-align: right">Robot Arm</td><td style="text-align: right">4800</td><td style="text-align: right">2397</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">9.14e+00</td><td style="text-align: right">1.83e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">5.66e+04</td></tr><tr><td style="text-align: right">Goddard Rocket</td><td style="text-align: right">2400</td><td style="text-align: right">1600</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.01e+00</td><td style="text-align: right">2.92e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">1.19e+00</td><td style="text-align: right">1.00e-02</td></tr><tr><td style="text-align: right">Goddard Rocket</td><td style="text-align: right">4800</td><td style="text-align: right">3200</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.01e+00</td><td style="text-align: right">2.92e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">1.00e+00</td><td style="text-align: right">1.00e-02</td></tr><tr><td style="text-align: right">Goddard Rocket</td><td style="text-align: right">9600</td><td style="text-align: right">6400</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">1.01e+00</td><td style="text-align: right">2.36e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">1.00e+00</td><td style="text-align: right">1.00e-02</td></tr><tr><td style="text-align: right">Particle Steering</td><td style="text-align: right">800</td><td style="text-align: right">400</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">5.55e-01</td><td style="text-align: right">1.03e+01</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">7.62e-12</td></tr><tr><td style="text-align: right">Particle Steering</td><td style="text-align: right">1600</td><td style="text-align: right">800</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">5.55e-01</td><td style="text-align: right">1.06e+00</td><td style="text-align: right">4</td><td style="text-align: right">4</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">6.15e-12</td></tr><tr><td style="text-align: right">Particle Steering</td><td style="text-align: right">3200</td><td style="text-align: right">1600</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">5.55e-01</td><td style="text-align: right">1.07e+00</td><td style="text-align: right">4</td><td style="text-align: right">4</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">5.94e-12</td></tr><tr><td style="text-align: right">Elastic-Plastic Torsion</td><td style="text-align: right">7802</td><td style="text-align: right">7802</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">-4.18e-01</td><td style="text-align: right">7.97e+01</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">2.00e-07</td><td style="text-align: right">1.01e-05</td></tr><tr><td style="text-align: right">Elastic-Plastic Torsion</td><td style="text-align: right">17327</td><td style="text-align: right">17327</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">-4.18e-01</td><td style="text-align: right">3.60e+02</td><td style="text-align: right">2</td><td style="text-align: right">2</td><td style="text-align: right">2.00e-07</td><td style="text-align: right">5.46e-06</td></tr><tr><td style="text-align: right">Elastic-Plastic Torsion</td><td style="text-align: right">30602</td><td style="text-align: right">30602</td><td style="text-align: right">max_time</td><td style="text-align: right">0.00e+00</td><td style="text-align: right">-4.18e-01</td><td style="text-align: right">1.14e+00</td><td style="text-align: right">1</td><td style="text-align: right">1</td><td style="text-align: right">1.00e+00</td><td style="text-align: right">5.05e-05</td></tr></table></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../tuto_rocket/">Rocket Control »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a 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href="#Contents">Contents</a><a id="Contents-1"></a><a class="docs-heading-anchor-permalink" href="#Contents" title="Permalink"></a></h2><p>​</p><ul><li><a href="#Reference">Reference</a></li><li class="no-marker"><ul><li><a href="#Contents">Contents</a></li><li><a href="#Index">Index</a></li></ul></li></ul><p>​</p><h2 id="Index"><a class="docs-heading-anchor" href="#Index">Index</a><a id="Index-1"></a><a class="docs-heading-anchor-permalink" href="#Index" title="Permalink"></a></h2><p>​</p><ul><li><a href="#PDEOptimizationProblems.meta"><code>PDEOptimizationProblems.meta</code></a></li><li><a href="#PDEOptimizationProblems.burger1d-Tuple"><code>PDEOptimizationProblems.burger1d</code></a></li><li><a href="#PDEOptimizationProblems.cellincrease-Tuple"><code>PDEOptimizationProblems.cellincrease</code></a></li><li><a href="#PDEOptimizationProblems.cellincrease_MichaelisMenten-Tuple"><code>PDEOptimizationProblems.cellincrease_MichaelisMenten</code></a></li><li><a href="#PDEOptimizationProblems.controlelasticmembrane1-Tuple"><code>PDEOptimizationProblems.controlelasticmembrane1</code></a></li><li><a href="#PDEOptimizationProblems.controlelasticmembrane2-Tuple{}"><code>PDEOptimizationProblems.controlelasticmembrane2</code></a></li><li><a href="#PDEOptimizationProblems.incompressiblenavierstokes-Tuple"><code>PDEOptimizationProblems.incompressiblenavierstokes</code></a></li><li><a href="#PDEOptimizationProblems.inversepoissonproblem2d-Tuple{}"><code>PDEOptimizationProblems.inversepoissonproblem2d</code></a></li><li><a href="#PDEOptimizationProblems.membrane-Tuple"><code>PDEOptimizationProblems.membrane</code></a></li><li><a href="#PDEOptimizationProblems.penalizedpoisson-Tuple"><code>PDEOptimizationProblems.penalizedpoisson</code></a></li><li><a href="#PDEOptimizationProblems.poisson3d-Tuple{}"><code>PDEOptimizationProblems.poisson3d</code></a></li><li><a href="#PDEOptimizationProblems.poissonboltzman2d-Tuple{}"><code>PDEOptimizationProblems.poissonboltzman2d</code></a></li><li><a href="#PDEOptimizationProblems.smallestlaplacianeigenvalue-Tuple{}"><code>PDEOptimizationProblems.smallestlaplacianeigenvalue</code></a></li></ul><p>​</p><article class="docstring"><header><a class="docstring-binding" id="PDEOptimizationProblems.meta" href="#PDEOptimizationProblems.meta"><code>PDEOptimizationProblems.meta</code></a> — <span class="docstring-category">Constant</span></header><section><div><pre><code class="language-julia hljs">PDEOptimizationProblems.meta</code></pre><p>A composite type that represents the main features of the PDE-constrained optimization problem.     optimize    ∫( f(θ, y, u) )dΩ     subject to  lvar ≤ (θ, y, u)    ≤ uvar                 ∫( res(θ, y, u, v) )dΩ = 0 –- The following keys are valid: Problem meta</p><ul><li><code>domaindim</code>: dimension of the domain 1/2/3 for 1D/2D/3D</li><li><code>pbtype</code>: in pbtypes</li><li><code>nθ</code>: size of the unknown vector</li><li><code>ny</code>: number of unknown function</li><li><code>nu</code>: number of control function</li></ul><p>Solution meta</p><ul><li><code>optimalvalue</code>: best known objective value (NaN if unknown, -Inf if unbounded problem)</li></ul><p>Classification</p><ul><li><code>objtype</code>: in objtypes</li><li><code>contype</code>: in contypes</li><li><code>origin</code>: in origins</li><li><code>has_cvx_obj</code>: true if the problem has a convex objective</li><li><code>has_cvx_con</code>: true if the problem has convex constraints</li><li><code>has_bounds</code>: true if the problem has bound constraints</li><li><code>has_fixed_variables</code>: true if it has fixed variables</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/tmigot/PDEOptimizationProblems/blob/bd4d2ab69c5641c40c9cebce45e4749cfdbb7d51/src/PDEOptimizationProblems.jl#L195-L219">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="PDEOptimizationProblems.burger1d-Tuple" href="#PDEOptimizationProblems.burger1d-Tuple"><code>PDEOptimizationProblems.burger1d</code></a> — <span class="docstring-category">Method</span></header><section><div><p><code>Burger1d(;n :: Int = 512, kwargs...)</code></p><p>Let Ω=(0,1), we solve the one-dimensional ODE-constrained control problem: min<em>{y,u}   0.5 ∫</em>Ω​ |y(x) - y<em>d(x)|^2dx + 0.5 * α * ∫</em>Ω​ |u|^2 s.t.          -ν y&#39;&#39; + yy&#39; = u + h,   for    x ∈  Ω,                   y(0) = 0, y(1)=-1,  for    x ∈ ∂Ω, where the constraint is a 1D stationary Burger&#39;s equation over Ω, with h(x)=2(ν + x^3) and ν=0.08. The first objective measures deviation from the data y_d(x)=-x^2, while the second term regularizes the control with α = 0.01.</p><p>This example has been used in, Section 9.1, Estrin, R., Friedlander, M. P., Orban, D., &amp; Saunders, M. A. (2020). Implementing a smooth exact penalty function for equality-constrained nonlinear optimization. SIAM Journal on Scientific Computing, 42(3), A1809-A1835.</p><p>The specificity of the problem:</p><ul><li>quadratic objective function;</li><li>nonlinear constraints with AD jacobian;</li></ul><p>Suggestions:</p><ul><li>FEOperatorFromTerms has only one term. We might consider splitting linear and</li></ul><p>nonlinear terms.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/tmigot/PDEOptimizationProblems/blob/bd4d2ab69c5641c40c9cebce45e4749cfdbb7d51/src/burger1d.jl#L3-L25">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="PDEOptimizationProblems.cellincrease-Tuple" href="#PDEOptimizationProblems.cellincrease-Tuple"><code>PDEOptimizationProblems.cellincrease</code></a> — <span class="docstring-category">Method</span></header><section><div><p>Mairet, F., &amp; Bayen, T. (2021). The promise of dawn: microalgae photoacclimation as an optimal control problem of resource allocation. Journal of Theoretical Biology, 515, 110597.</p><p>Using a photosynthetic rate proportional to the photosynthetic apparatus mass fraction.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/tmigot/PDEOptimizationProblems/blob/bd4d2ab69c5641c40c9cebce45e4749cfdbb7d51/src/cellincrease.jl#L3-L7">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="PDEOptimizationProblems.cellincrease_MichaelisMenten-Tuple" href="#PDEOptimizationProblems.cellincrease_MichaelisMenten-Tuple"><code>PDEOptimizationProblems.cellincrease_MichaelisMenten</code></a> — <span class="docstring-category">Method</span></header><section><div><p>Mairet, F., &amp; Bayen, T. (2021). The promise of dawn: microalgae photoacclimation as an optimal control problem of resource allocation. Journal of Theoretical Biology, 515, 110597.</p><p>Using Michaelis-Menten&#39;s function for the photosynthetic rate.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/tmigot/PDEOptimizationProblems/blob/bd4d2ab69c5641c40c9cebce45e4749cfdbb7d51/src/cellincrease_MichaelisMenten.jl#L3-L7">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="PDEOptimizationProblems.controlelasticmembrane1-Tuple" href="#PDEOptimizationProblems.controlelasticmembrane1-Tuple"><code>PDEOptimizationProblems.controlelasticmembrane1</code></a> — <span class="docstring-category">Method</span></header><section><div><p><code>controlelasticmembrane1(; n :: Int = 10, args...)</code></p><p>Let Ω = (-1,1)^2, we solve the following distributed Poisson control problem with Dirichlet boundary:</p><p>min<em>{y ∈ H^1</em>0,u ∈ H^1}   0.5 ∫<em>Ω​ |y(x) - yd(x)|^2dx + 0.5 * α * ∫</em>Ω​ |u|^2  s.t.         -Δy = h + u,   for    x ∈  Ω                y  = 0,       for    x ∈ ∂Ω               umin(x) &lt;=  u(x) &lt;= umax(x) where yd(x) = -x[1]^2 and α = 1e-2. The force term is h(x<em>1,x</em>2) = - sin( ω x<em>1)sin( ω x</em>2) with  ω = π - 1/8. In this first case, the bound constraints are constants with umin(x) = 0.0 and umax(x) = 1.0.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/tmigot/PDEOptimizationProblems/blob/bd4d2ab69c5641c40c9cebce45e4749cfdbb7d51/src/controlelasticmembrane1.jl#L3-L18">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="PDEOptimizationProblems.controlelasticmembrane2-Tuple{}" href="#PDEOptimizationProblems.controlelasticmembrane2-Tuple{}"><code>PDEOptimizationProblems.controlelasticmembrane2</code></a> — <span class="docstring-category">Method</span></header><section><div><p><code>controlelasticmembrane2(; n :: Int = 10, args...)</code></p><p>Let Ω = (-1,1)^2, we solve the following distributed Poisson control problem with Dirichlet boundary:</p><p>min<em>{y ∈ H^1</em>0,u ∈ H^1}   0.5 ∫<em>Ω​ |y(x) - yd(x)|^2dx + 0.5 * α * ∫</em>Ω​ |u|^2  s.t.         -Δy = h + u,   for    x ∈  Ω                y  = 0,       for    x ∈ ∂Ω               u<em>min(x) &lt;=  u(x) &lt;= u</em>max(x) where yd(x) = -x[1]^2 and α = 1e-2. The force term is h(x<em>1,x</em>2) = - sin( ω x<em>1)sin( ω x</em>2) with  ω = π - 1/8. In this second case, the bound constraints are umin(x) = x<em>1+x</em>2 and umax(x) = x<em>1^2+x</em>2^2 applied at the midpoint of the cells.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/tmigot/PDEOptimizationProblems/blob/bd4d2ab69c5641c40c9cebce45e4749cfdbb7d51/src/controlelasticmembrane2.jl#L3-L17">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="PDEOptimizationProblems.incompressiblenavierstokes-Tuple" href="#PDEOptimizationProblems.incompressiblenavierstokes-Tuple"><code>PDEOptimizationProblems.incompressiblenavierstokes</code></a> — <span class="docstring-category">Method</span></header><section><div><p><code>incompressibleNavierStokes(; n :: Int64 = 3, kargs...)</code></p><p>This corresponds to the incompressible Navier-Stokes equation described in the Gridap Tutorials: https://gridap.github.io/Tutorials/stable/pages/t008<em>inc</em>navier_stokes/</p><p>It has no objective function and no control, just the PDE.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/tmigot/PDEOptimizationProblems/blob/bd4d2ab69c5641c40c9cebce45e4749cfdbb7d51/src/incompressibleNavierStokes.jl#L3-L12">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="PDEOptimizationProblems.inversepoissonproblem2d-Tuple{}" href="#PDEOptimizationProblems.inversepoissonproblem2d-Tuple{}"><code>PDEOptimizationProblems.inversepoissonproblem2d</code></a> — <span class="docstring-category">Method</span></header><section><div><p><code>inversePoissonproblem2d(;n :: Int = 512, kwargs...)</code></p><p>Let Ω=(-1,1)^2, we solve the 2-dimensional PDE-constrained control problem: min<em>{y ∈ H</em>1^0, u ∈ L^∞}   0.5 ∫<em>Ω​ |y(x) - y</em>d(x)|^2dx + 0.5 * α * ∫<em>Ω​ |u|^2 s.t.          -∇⋅(z∇u) = h,   for    x ∈  Ω,                   u(x) = 0,   for    x ∈ ∂Ω. Let c = (0.2,0.2) and and define S</em>1 = {x | ||x-c||<em>2 ≤ 0.3 } and S</em>2 = {x | ||x-c||<em>1 ≤ 0.6 }. The target u</em>d is generated as the solution of the PDE with z<em>*(x) = 1 + 0.5 * I</em>{S<em>1}(x) + 0.5 * I</em>{S<em>2}(x). The force term here is h(x</em>1,x<em>2) = - sin( ω x</em>1)sin( ω x<em>2) with  ω = π - 1/8. The control variable z represents the diffusion coefficients for the Poisson problem that we are trying to recover. Set α = 10^{-4} and discretize using P1 finite elements on a uniform mesh of 1089 triangles and employ an identical discretization for the optimization variables u, thus n</em>con = 1089 and n<em>pde = 961. Initial point is y</em>0=1 and u_0 = 1. z ≥ 0 (implicit)</p><p>This example has been used in, Section 9.2, Estrin, R., Friedlander, M. P., Orban, D., &amp; Saunders, M. A. (2020). Implementing a smooth exact penalty function for equality-constrained nonlinear optimization. SIAM Journal on Scientific Computing, 42(3), A1809-A1835.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/tmigot/PDEOptimizationProblems/blob/bd4d2ab69c5641c40c9cebce45e4749cfdbb7d51/src/inversepoissonproblem2d.jl#L9-L30">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="PDEOptimizationProblems.membrane-Tuple" href="#PDEOptimizationProblems.membrane-Tuple"><code>PDEOptimizationProblems.membrane</code></a> — <span class="docstring-category">Method</span></header><section><div><p>https://arxiv.org/pdf/2103.14552.pdf Example 1. MEMBRANE Multilevel Active-Set Trust-Region (MASTR) Method for Bound Constrained Minimization Alena Kopaničáková and Rolf Krause</p><p>The solution and original problem is given in Domorádová, M., &amp; Dostál, Z. (2007). Projector preconditioning for partially bound‐constrained quadratic optimization. Numerical Linear Algebra with Applications, 14(10), 791-806.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/tmigot/PDEOptimizationProblems/blob/bd4d2ab69c5641c40c9cebce45e4749cfdbb7d51/src/membrane.jl#L3-L11">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="PDEOptimizationProblems.penalizedpoisson-Tuple" href="#PDEOptimizationProblems.penalizedpoisson-Tuple"><code>PDEOptimizationProblems.penalizedpoisson</code></a> — <span class="docstring-category">Method</span></header><section><div><p>Let Ω=(0,1)^2, we solve the unconstrained optimization problem: min<em>{u ∈ H</em>1^0}   0.5 ∫_Ω​ |∇u|^2 - w u dx s.t.              u(x) = 0,     for    x ∈ ∂Ω whre w(x)=1.0.</p><p>The minimizer of this problem is the solution of the Poisson equation:  ∫_Ω​ (∇u ∇v - f*v)dx = 0, ∀ v ∈ Ω  u = 0, x ∈ ∂Ω</p><p>This example has been used in Exercice 10.2.4 (p. 308) of G. Allaire, Analyse numérique et optimisation, Les éditions de Polytechnique</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/tmigot/PDEOptimizationProblems/blob/bd4d2ab69c5641c40c9cebce45e4749cfdbb7d51/src/penalizedpoisson.jl#L3-L14">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="PDEOptimizationProblems.poisson3d-Tuple{}" href="#PDEOptimizationProblems.poisson3d-Tuple{}"><code>PDEOptimizationProblems.poisson3d</code></a> — <span class="docstring-category">Method</span></header><section><div><p><code>poisson3d(; n :: Int = 10)</code></p><p>This example represents a Poisson equation with Dirichlet boundary conditions over the 3d-box, (0,1)^3, and we minimize the squared H_1-norm to a manufactured solution. So, the minimal value is expected to be 0.</p><p>It is inspired from the 2nd tutorial in Gridap.jl: https://gridap.github.io/Tutorials/stable/pages/t002_validation/</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/tmigot/PDEOptimizationProblems/blob/bd4d2ab69c5641c40c9cebce45e4749cfdbb7d51/src/poisson3d.jl#L3-L12">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="PDEOptimizationProblems.poissonboltzman2d-Tuple{}" href="#PDEOptimizationProblems.poissonboltzman2d-Tuple{}"><code>PDEOptimizationProblems.poissonboltzman2d</code></a> — <span class="docstring-category">Method</span></header><section><div><p><code>poissonBoltzman2d(; n :: Int = 100)</code></p><p>Let Ω=(-1,1)^2, we solve the 2-dimensional PDE-constrained control problem: min<em>{y ∈ H</em>1^0, u ∈ L^∞}   0.5 ∫<em>Ω​ |y(x) - yd(x)|^2dx + 0.5 * α * ∫</em>Ω​ |u|^2  s.t.         -Δy + sinh(y) = h + u,   for    x ∈  Ω                          y(x) = 0,     for    x ∈ ∂Ω</p><p>The force term here is h(x<em>1,x</em>2) = - sin( ω x<em>1)sin( ω x</em>2) with  ω = π - 1/8. The targeted function is yd(x) = {10 if x ∈ [0.25,0.75]^2, 5 otherwise}. We discretize using P1 finite elements on a uniform mesh with 10201 triangles, resulting in a problem with n = 20002 variables and m = 9801 constraints. We use y<em>0=1 and u</em>0 = 1 as the initial point.</p><p>This example has been used in, Section 9.3, Estrin, R., Friedlander, M. P., Orban, D., &amp; Saunders, M. A. (2020). Implementing a smooth exact penalty function for equality-constrained nonlinear optimization. SIAM Journal on Scientific Computing, 42(3), A1809-A1835.</p><p>The specificity of the problem:</p><ul><li>quadratic objective function;</li><li>nonlinear constraints with AD jacobian;</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/tmigot/PDEOptimizationProblems/blob/bd4d2ab69c5641c40c9cebce45e4749cfdbb7d51/src/poissonboltzman2d.jl#L3-L26">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="PDEOptimizationProblems.smallestlaplacianeigenvalue-Tuple{}" href="#PDEOptimizationProblems.smallestlaplacianeigenvalue-Tuple{}"><code>PDEOptimizationProblems.smallestlaplacianeigenvalue</code></a> — <span class="docstring-category">Method</span></header><section><div><p><code>smallestLaplacianeigenvalue(; n :: Int = 10, args...)</code></p><p>We solve the following problem:</p><p>min<em>{u,z}   ∫</em>Ω​ |∇u|^2  s.t.        ∫_Ω​ u^2 = 1,     for    x ∈  Ω                 u    = 0,     for    x ∈ ∂Ω</p><p>The solution is an eigenvector of the smallest eigenvalue of the Laplacian operator,  given by the value of the objective function.  λ is an eigenvalue of the Laplacian if there exists u such that</p><p>Δu + λ u = 0,   for    x ∈  Ω         u = 0,   for    x ∈ ∂Ω</p><p>This example has been used in Exercice 10.2.11 (p. 313) of G. Allaire, Analyse numérique et optimisation, Les éditions de Polytechnique and more eigenvalue problems can be found in Section 7.3.2</p><p>TODO:</p><ul><li>does the 1 work as it is? or should it be put in lcon, ucon?</li><li>it is 1D for now.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/tmigot/PDEOptimizationProblems/blob/bd4d2ab69c5641c40c9cebce45e4749cfdbb7d51/src/smallestlaplacianeigenvalue.jl#L3-L25">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../tuto_rocket/">« Rocket Control</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Saturday 2 March 2024 22:37">Saturday 2 March 2024</span>. 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+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Search · PDEOptimizationProblems</title><script data-outdated-warner src="../assets/warner.js"></script><link rel="canonical" href="https://tmigot.github.io/PDEOptimizationProblems/search/"/><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script><link href="../assets/style.css" rel="stylesheet" type="text/css"/></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../"><img src="../assets/logo.png" alt="PDEOptimizationProblems logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../">PDEOptimizationProblems</a></span></div><form class="docs-search" action><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><a class="tocitem" href="../cops/">COPS</a></li><li><a class="tocitem" href="../tuto_rocket/">Rocket Control</a></li><li><a class="tocitem" href="../reference/">Reference</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Search</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Search</a></li></ul></nav><div class="docs-right"><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article><p id="documenter-search-info">Loading search...</p><ul id="documenter-search-results"></ul></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Saturday 2 March 2024 22:37">Saturday 2 March 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body><script src="../search_index.js"></script><script src="../assets/search.js"></script></html>
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+[{"location":"tuto_rocket/#Goddard-Rocket-Control","page":"Rocket Control","title":"Goddard Rocket Control","text":"","category":"section"},{"location":"tuto_rocket/","page":"Rocket Control","title":"Rocket Control","text":"using Gridap, PDENLPModels, PDEOptimizationProblems","category":"page"},{"location":"tuto_rocket/","page":"Rocket Control","title":"Rocket Control","text":"This tutorial shows how to solve a nonlinear rocketry control problem.  The problem was drawn from the COPS3 benchmark, and was used in JuMP's tutorials rocket control.","category":"page"},{"location":"tuto_rocket/","page":"Rocket Control","title":"Rocket Control","text":"PDEOptimizationProblems contains a list of predefined PDE-constrained optimization problems, e.g. Goddard rocket control problem via the function rocket. Note that the models in PDEOptimizationProblems are in Lagrangian form, so the implementation considers a Mayer to Lagrange formulation that adds an additional (constant) function H := h(T) see in the code.","category":"page"},{"location":"tuto_rocket/","page":"Rocket Control","title":"Rocket Control","text":"T = 0.2 # final time\nn = 800 # number of cells\n\nnlp = rocket(n = n, T = T)","category":"page"},{"location":"tuto_rocket/","page":"Rocket Control","title":"Rocket Control","text":"The return model is a GridapPDENLPModel and, in particular, is an instance of an AbstractNLPModel that can be solved with any tool from the JuliaSmoothOptimizers organization. Then, using NLPModelsIpopt.jl, we solve the model and get the required information.","category":"page"},{"location":"tuto_rocket/","page":"Rocket Control","title":"Rocket Control","text":"using NLPModelsIpopt\n\nstats = ipopt(nlp, x0 = nlp.meta.x0)\nobj_ipopt, con_ipopt = stats.objective, stats.primal_feas\n(hh, Hh, vh, mh), uh = split_vectors(nlp, stats.solution)","category":"page"},{"location":"tuto_rocket/","page":"Rocket Control","title":"Rocket Control","text":"Finally, we can plot the functions, and the results match JuMP's tutorial and COPS 3 report.","category":"page"},{"location":"tuto_rocket/","page":"Rocket Control","title":"Rocket Control","text":"using Plots\ngr()\n\nh₀, m₀, mᵪ = 1.0, 1.0, 0.6\np = Plots.plot(\n  Plots.plot(0:T/n:T, vcat(h₀, hh); xlabel = \"Time (s)\", ylabel = \"Altitude\"),\n  Plots.plot(0:T/n:T, vcat(m₀, mh, mᵪ * m₀); xlabel = \"Time (s)\", ylabel = \"Mass\"),\n  Plots.plot(0:T/n:T, vcat(0., vh); xlabel = \"Time (s)\", ylabel = \"Velocity\"),\n  Plots.plot(0:T/(length(uh) - 1):T, uh; xlabel = \"Time (s)\", ylabel = \"Thrust\"),\n  layout = (2, 2),\n  legend = false,\n  margin = 1Plots.cm,\n)","category":"page"},{"location":"tuto_rocket/","page":"Rocket Control","title":"Rocket Control","text":"An alternative is also to intepolate the entire solution over the domain as an FEFunction (Gridap's function type) and save the interpolation in a VTK file.","category":"page"},{"location":"tuto_rocket/","page":"Rocket Control","title":"Rocket Control","text":"Ypde = nlp.pdemeta.Ypde\nh_h  = FEFunction(Ypde.spaces[1], hh)\nH_h  = FEFunction(Ypde.spaces[2], Hh)\nv_h  = FEFunction(Ypde.spaces[3], vh)\nm_h  = FEFunction(Ypde.spaces[4], mh)\nu_h  = FEFunction(nlp.pdemeta.Ycon, uh)\n\nwritevtk(\n  nlp.pdemeta.tnrj.trian,\n  \"results_robot\",\n  cellfields=[\"uh\" => u_h, \"hh\" => h_h, \"Hh\" => H_h, \"vh\" => v_h, \"mh\" => m_h],\n)","category":"page"},{"location":"reference/#Reference","page":"Reference","title":"Reference","text":"","category":"section"},{"location":"reference/","page":"Reference","title":"Reference","text":"​","category":"page"},{"location":"reference/#Contents","page":"Reference","title":"Contents","text":"","category":"section"},{"location":"reference/","page":"Reference","title":"Reference","text":"​","category":"page"},{"location":"reference/","page":"Reference","title":"Reference","text":"Pages = [\"reference.md\"]","category":"page"},{"location":"reference/","page":"Reference","title":"Reference","text":"​","category":"page"},{"location":"reference/#Index","page":"Reference","title":"Index","text":"","category":"section"},{"location":"reference/","page":"Reference","title":"Reference","text":"​","category":"page"},{"location":"reference/","page":"Reference","title":"Reference","text":"Pages = [\"reference.md\"]","category":"page"},{"location":"reference/","page":"Reference","title":"Reference","text":"​","category":"page"},{"location":"reference/","page":"Reference","title":"Reference","text":"Modules = [PDEOptimizationProblems]","category":"page"},{"location":"reference/#PDEOptimizationProblems.meta","page":"Reference","title":"PDEOptimizationProblems.meta","text":"PDEOptimizationProblems.meta\n\nA composite type that represents the main features of the PDE-constrained optimization problem.     optimize    ∫( f(θ, y, u) )dΩ     subject to  lvar ≤ (θ, y, u)    ≤ uvar                 ∫( res(θ, y, u, v) )dΩ = 0 –- The following keys are valid: Problem meta\n\ndomaindim: dimension of the domain 1/2/3 for 1D/2D/3D\npbtype: in pbtypes\nnθ: size of the unknown vector\nny: number of unknown function\nnu: number of control function\n\nSolution meta\n\noptimalvalue: best known objective value (NaN if unknown, -Inf if unbounded problem)\n\nClassification\n\nobjtype: in objtypes\ncontype: in contypes\norigin: in origins\nhas_cvx_obj: true if the problem has a convex objective\nhas_cvx_con: true if the problem has convex constraints\nhas_bounds: true if the problem has bound constraints\nhas_fixed_variables: true if it has fixed variables\n\n\n\n\n\n","category":"constant"},{"location":"reference/#PDEOptimizationProblems.burger1d-Tuple","page":"Reference","title":"PDEOptimizationProblems.burger1d","text":"Burger1d(;n :: Int = 512, kwargs...)\n\nLet Ω=(0,1), we solve the one-dimensional ODE-constrained control problem: min{y,u}   0.5 ∫Ω​ |y(x) - yd(x)|^2dx + 0.5 * α * ∫Ω​ |u|^2 s.t.          -ν y'' + yy' = u + h,   for    x ∈  Ω,                   y(0) = 0, y(1)=-1,  for    x ∈ ∂Ω, where the constraint is a 1D stationary Burger's equation over Ω, with h(x)=2(ν + x^3) and ν=0.08. The first objective measures deviation from the data y_d(x)=-x^2, while the second term regularizes the control with α = 0.01.\n\nThis example has been used in, Section 9.1, Estrin, R., Friedlander, M. P., Orban, D., & Saunders, M. A. (2020). Implementing a smooth exact penalty function for equality-constrained nonlinear optimization. SIAM Journal on Scientific Computing, 42(3), A1809-A1835.\n\nThe specificity of the problem:\n\nquadratic objective function;\nnonlinear constraints with AD jacobian;\n\nSuggestions:\n\nFEOperatorFromTerms has only one term. We might consider splitting linear and\n\nnonlinear terms.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDEOptimizationProblems.cellincrease-Tuple","page":"Reference","title":"PDEOptimizationProblems.cellincrease","text":"Mairet, F., & Bayen, T. (2021). The promise of dawn: microalgae photoacclimation as an optimal control problem of resource allocation. Journal of Theoretical Biology, 515, 110597.\n\nUsing a photosynthetic rate proportional to the photosynthetic apparatus mass fraction.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDEOptimizationProblems.cellincrease_MichaelisMenten-Tuple","page":"Reference","title":"PDEOptimizationProblems.cellincrease_MichaelisMenten","text":"Mairet, F., & Bayen, T. (2021). The promise of dawn: microalgae photoacclimation as an optimal control problem of resource allocation. Journal of Theoretical Biology, 515, 110597.\n\nUsing Michaelis-Menten's function for the photosynthetic rate.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDEOptimizationProblems.controlelasticmembrane1-Tuple","page":"Reference","title":"PDEOptimizationProblems.controlelasticmembrane1","text":"controlelasticmembrane1(; n :: Int = 10, args...)\n\nLet Ω = (-1,1)^2, we solve the following distributed Poisson control problem with Dirichlet boundary:\n\nmin{y ∈ H^10,u ∈ H^1}   0.5 ∫Ω​ |y(x) - yd(x)|^2dx + 0.5 * α * ∫Ω​ |u|^2  s.t.         -Δy = h + u,   for    x ∈  Ω                y  = 0,       for    x ∈ ∂Ω               umin(x) <=  u(x) <= umax(x) where yd(x) = -x[1]^2 and α = 1e-2. The force term is h(x1,x2) = - sin( ω x1)sin( ω x2) with  ω = π - 1/8. In this first case, the bound constraints are constants with umin(x) = 0.0 and umax(x) = 1.0.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDEOptimizationProblems.controlelasticmembrane2-Tuple{}","page":"Reference","title":"PDEOptimizationProblems.controlelasticmembrane2","text":"controlelasticmembrane2(; n :: Int = 10, args...)\n\nLet Ω = (-1,1)^2, we solve the following distributed Poisson control problem with Dirichlet boundary:\n\nmin{y ∈ H^10,u ∈ H^1}   0.5 ∫Ω​ |y(x) - yd(x)|^2dx + 0.5 * α * ∫Ω​ |u|^2  s.t.         -Δy = h + u,   for    x ∈  Ω                y  = 0,       for    x ∈ ∂Ω               umin(x) <=  u(x) <= umax(x) where yd(x) = -x[1]^2 and α = 1e-2. The force term is h(x1,x2) = - sin( ω x1)sin( ω x2) with  ω = π - 1/8. In this second case, the bound constraints are umin(x) = x1+x2 and umax(x) = x1^2+x2^2 applied at the midpoint of the cells.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDEOptimizationProblems.incompressiblenavierstokes-Tuple","page":"Reference","title":"PDEOptimizationProblems.incompressiblenavierstokes","text":"incompressibleNavierStokes(; n :: Int64 = 3, kargs...)\n\nThis corresponds to the incompressible Navier-Stokes equation described in the Gridap Tutorials: https://gridap.github.io/Tutorials/stable/pages/t008incnavier_stokes/\n\nIt has no objective function and no control, just the PDE.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDEOptimizationProblems.inversepoissonproblem2d-Tuple{}","page":"Reference","title":"PDEOptimizationProblems.inversepoissonproblem2d","text":"inversePoissonproblem2d(;n :: Int = 512, kwargs...)\n\nLet Ω=(-1,1)^2, we solve the 2-dimensional PDE-constrained control problem: min{y ∈ H1^0, u ∈ L^∞}   0.5 ∫Ω​ |y(x) - yd(x)|^2dx + 0.5 * α * ∫Ω​ |u|^2 s.t.          -∇⋅(z∇u) = h,   for    x ∈  Ω,                   u(x) = 0,   for    x ∈ ∂Ω. Let c = (0.2,0.2) and and define S1 = {x | ||x-c||2 ≤ 0.3 } and S2 = {x | ||x-c||1 ≤ 0.6 }. The target ud is generated as the solution of the PDE with z*(x) = 1 + 0.5 * I{S1}(x) + 0.5 * I{S2}(x). The force term here is h(x1,x2) = - sin( ω x1)sin( ω x2) with  ω = π - 1/8. The control variable z represents the diffusion coefficients for the Poisson problem that we are trying to recover. Set α = 10^{-4} and discretize using P1 finite elements on a uniform mesh of 1089 triangles and employ an identical discretization for the optimization variables u, thus ncon = 1089 and npde = 961. Initial point is y0=1 and u_0 = 1. z ≥ 0 (implicit)\n\nThis example has been used in, Section 9.2, Estrin, R., Friedlander, M. P., Orban, D., & Saunders, M. A. (2020). Implementing a smooth exact penalty function for equality-constrained nonlinear optimization. SIAM Journal on Scientific Computing, 42(3), A1809-A1835.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDEOptimizationProblems.membrane-Tuple","page":"Reference","title":"PDEOptimizationProblems.membrane","text":"https://arxiv.org/pdf/2103.14552.pdf Example 1. MEMBRANE Multilevel Active-Set Trust-Region (MASTR) Method for Bound Constrained Minimization Alena Kopaničáková and Rolf Krause\n\nThe solution and original problem is given in Domorádová, M., & Dostál, Z. (2007). Projector preconditioning for partially bound‐constrained quadratic optimization. Numerical Linear Algebra with Applications, 14(10), 791-806.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDEOptimizationProblems.penalizedpoisson-Tuple","page":"Reference","title":"PDEOptimizationProblems.penalizedpoisson","text":"Let Ω=(0,1)^2, we solve the unconstrained optimization problem: min{u ∈ H1^0}   0.5 ∫_Ω​ |∇u|^2 - w u dx s.t.              u(x) = 0,     for    x ∈ ∂Ω whre w(x)=1.0.\n\nThe minimizer of this problem is the solution of the Poisson equation:  ∫_Ω​ (∇u ∇v - f*v)dx = 0, ∀ v ∈ Ω  u = 0, x ∈ ∂Ω\n\nThis example has been used in Exercice 10.2.4 (p. 308) of G. Allaire, Analyse numérique et optimisation, Les éditions de Polytechnique\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDEOptimizationProblems.poisson3d-Tuple{}","page":"Reference","title":"PDEOptimizationProblems.poisson3d","text":"poisson3d(; n :: Int = 10)\n\nThis example represents a Poisson equation with Dirichlet boundary conditions over the 3d-box, (0,1)^3, and we minimize the squared H_1-norm to a manufactured solution. So, the minimal value is expected to be 0.\n\nIt is inspired from the 2nd tutorial in Gridap.jl: https://gridap.github.io/Tutorials/stable/pages/t002_validation/\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDEOptimizationProblems.poissonboltzman2d-Tuple{}","page":"Reference","title":"PDEOptimizationProblems.poissonboltzman2d","text":"poissonBoltzman2d(; n :: Int = 100)\n\nLet Ω=(-1,1)^2, we solve the 2-dimensional PDE-constrained control problem: min{y ∈ H1^0, u ∈ L^∞}   0.5 ∫Ω​ |y(x) - yd(x)|^2dx + 0.5 * α * ∫Ω​ |u|^2  s.t.         -Δy + sinh(y) = h + u,   for    x ∈  Ω                          y(x) = 0,     for    x ∈ ∂Ω\n\nThe force term here is h(x1,x2) = - sin( ω x1)sin( ω x2) with  ω = π - 1/8. The targeted function is yd(x) = {10 if x ∈ [0.25,0.75]^2, 5 otherwise}. We discretize using P1 finite elements on a uniform mesh with 10201 triangles, resulting in a problem with n = 20002 variables and m = 9801 constraints. We use y0=1 and u0 = 1 as the initial point.\n\nThis example has been used in, Section 9.3, Estrin, R., Friedlander, M. P., Orban, D., & Saunders, M. A. (2020). Implementing a smooth exact penalty function for equality-constrained nonlinear optimization. SIAM Journal on Scientific Computing, 42(3), A1809-A1835.\n\nThe specificity of the problem:\n\nquadratic objective function;\nnonlinear constraints with AD jacobian;\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDEOptimizationProblems.smallestlaplacianeigenvalue-Tuple{}","page":"Reference","title":"PDEOptimizationProblems.smallestlaplacianeigenvalue","text":"smallestLaplacianeigenvalue(; n :: Int = 10, args...)\n\nWe solve the following problem:\n\nmin{u,z}   ∫Ω​ |∇u|^2  s.t.        ∫_Ω​ u^2 = 1,     for    x ∈  Ω                 u    = 0,     for    x ∈ ∂Ω\n\nThe solution is an eigenvector of the smallest eigenvalue of the Laplacian operator,  given by the value of the objective function.  λ is an eigenvalue of the Laplacian if there exists u such that\n\nΔu + λ u = 0,   for    x ∈  Ω         u = 0,   for    x ∈ ∂Ω\n\nThis example has been used in Exercice 10.2.11 (p. 313) of G. Allaire, Analyse numérique et optimisation, Les éditions de Polytechnique and more eigenvalue problems can be found in Section 7.3.2\n\nTODO:\n\ndoes the 1 work as it is? or should it be put in lcon, ucon?\nit is 1D for now.\n\n\n\n\n\n","category":"method"},{"location":"cops/#Simulations-on-COPS-3-test-set","page":"COPS","title":"Simulations on COPS 3 test set","text":"","category":"section"},{"location":"cops/","page":"COPS","title":"COPS","text":"We run DCISolver.jl and NLPModelsIpopt.jl and NLPModelsKnitro.jl on an infinite-dimensional implementation of test problems from COPS 3.0 test set.","category":"page"},{"location":"cops/#DCILDL","page":"COPS","title":"DCILDL","text":"","category":"section"},{"location":"cops/","page":"COPS","title":"COPS","text":"name nvar ncon status objective opt_val time (s) #f #c dual_feas feas\nIsometrization of α-pinene 505 500 max_time 0.00e+00 1.99e+01 8.49e+00 2 2 0.00e+00 2.84e+01\nIsometrization of α-pinene 1005 1000 max_time 0.00e+00 1.99e+01 4.05e+00 2 2 0.00e+00 2.84e+01\nIsometrization of α-pinene 2005 2000 max_time 0.00e+00 1.99e+01 4.42e+00 2 2 0.00e+00 2.84e+01\nJournal Bearing 2600 0 exception Inf -1.55e-01 Inf 0 0 Inf Inf\nJournal Bearing 5775 0 exception Inf -1.55e-01 Inf 0 0 Inf Inf\nJournal Bearing 10200 0 exception Inf -1.55e-01 Inf 0 0 Inf Inf\nCatalyst Mixing 602 402 max_time 0.00e+00 -4.81e-02 9.96e+01 1 1 1.41e-01 2.50e-01\nCatalyst Mixing 1202 802 max_time 0.00e+00 -4.81e-02 3.94e+00 1 1 9.98e-02 2.50e-01\nCatalyst Mixing 2402 1602 max_time 0.00e+00 -4.81e-02 1.07e+03 2 2 7.07e-02 2.50e-01\nFlow in a Channel 800 800 max_time 0.00e+00 1.00e+00 5.14e+00 2 2 0.00e+00 2.20e-01\nFlow in a Channel 1600 1600 max_time 0.00e+00 1.00e+00 2.57e+00 2 2 0.00e+00 2.20e-01\nFlow in a Channel 3200 3200 max_time 0.00e+00 1.00e+00 2.78e+00 2 2 0.00e+00 2.20e-01\nTransition States for the Dirichlet Problem 9 0 first_order 0.00e+00 1.94e-06 0.00e+00 1 1 0.00e+00 0.00e+00\nTransition States for the Dirichlet Problem 19 0 first_order 0.00e+00 1.71e-02 0.00e+00 1 1 0.00e+00 0.00e+00\nTransition States for the Dirichlet Problem 39 0 first_order 0.00e+00 3.29e-02 0.00e+00 1 1 0.00e+00 0.00e+00\nCatalytic Cracking of Gas Oil 205 202 max_time 8.21e-02 5.24e-03 6.83e+01 1 1 4.19e-02 0.00e+00\nCatalytic Cracking of Gas Oil 405 402 max_time 8.11e-02 5.24e-03 1.11e+00 1 1 2.97e-02 0.00e+00\nCatalytic Cracking of Gas Oil 805 802 max_time 8.11e-02 5.24e-03 2.21e+00 1 1 2.10e-02 0.00e+00\nHang Glider 698 498 max_time -9.50e+02 1.25e+03 4.51e+03 2 2 4.75e-15 8.79e+01\nHang Glider 1398 998 max_time -9.50e+02 1.25e+03 8.86e+03 2 2 6.76e-15 6.44e+01\nHang Glider 2798 1998 max_time -9.50e+02 1.25e+03 1.77e+04 2 2 5.05e-09 4.66e+01\nTransition States for the Henon Problem 9 0 first_order 0.00e+00 7.22e+00 0.00e+00 1 1 0.00e+00 0.00e+00\nTransition States for the Henon Problem 19 0 first_order 0.00e+00 7.52e+01 0.00e+00 1 1 0.00e+00 0.00e+00\nTransition States for the Henon Problem 39 0 first_order 0.00e+00 1.26e+02 0.00e+00 1 1 0.00e+00 0.00e+00\nTransition States for the Lane-Emden Problem 9 0 first_order 0.00e+00 8.49e+00 0.00e+00 1 1 0.00e+00 0.00e+00\nTransition States for the Lane-Emden Problem 19 0 first_order 0.00e+00 9.11e+00 0.00e+00 1 1 0.00e+00 0.00e+00\nTransition States for the Lane-Emden Problem 39 0 first_order 0.00e+00 9.28e+00 0.00e+00 1 1 0.00e+00 0.00e+00\nMethanol to Hydrocarbons 308 303 exception Inf 9.02e-03 Inf 0 0 Inf Inf\nMethanol to Hydrocarbons 608 603 exception Inf 9.02e-03 Inf 0 0 Inf Inf\nMethanol to Hydrocarbons 1208 1203 exception Inf 9.02e-03 Inf 0 0 Inf Inf\nMinimal Surface with Obstacle 5002 2401 max_time 2.33e+00 2.51e+00 1.94e+01 1 1 6.85e-02 7.34e-03\nMinimal Surface with Obstacle 11252 5476 max_time 2.32e+00 2.51e+00 1.59e+00 2 2 5.29e-02 5.08e-03\nMinimal Surface with Obstacle 20002 9801 max_time 2.33e+00 2.51e+00 2.33e+00 2 2 4.44e-02 3.84e-03\nRobot Arm 1200 597 max_time 0.00e+00 9.14e+00 3.74e+00 2 2 0.00e+00 2.01e+04\nRobot Arm 2400 1197 max_time 0.00e+00 9.14e+00 3.87e+00 2 2 0.00e+00 4.02e+04\nRobot Arm 4800 2397 max_time 0.00e+00 9.14e+00 4.08e+00 2 2 0.00e+00 8.04e+04\nGoddard Rocket 2400 1600 max_time -1.00e+00 1.01e+00 4.83e+04 2 2 1.85e-02 2.64e-01\nGoddard Rocket 4800 3200 max_time -1.00e+00 1.01e+00 5.78e+04 2 2 1.32e-02 1.90e-01\nGoddard Rocket 9600 6400 max_time -1.00e+00 1.01e+00 1.23e+05 2 2 9.39e-03 1.69e-01\nParticle Steering 800 400 max_time 0.00e+00 5.55e-01 5.91e+01 2 2 0.00e+00 1.35e+01\nParticle Steering 1600 800 max_time 0.00e+00 5.55e-01 1.80e+02 2 2 0.00e+00 9.56e+00\nParticle Steering 3200 1600 max_time 0.00e+00 5.55e-01 6.38e+02 2 2 0.00e+00 6.79e+00\nElastic-Plastic Torsion 7802 7802 max_time 0.00e+00 -4.18e-01 5.58e+01 1 1 5.72e-02 9.93e-03\nElastic-Plastic Torsion 17327 17327 max_time 0.00e+00 -4.18e-01 2.22e+00 1 1 3.82e-02 6.64e-03\nElastic-Plastic Torsion 30602 30602 max_time 0.00e+00 -4.18e-01 2.71e+00 1 1 2.87e-02 4.98e-03","category":"page"},{"location":"cops/#knitro","page":"COPS","title":"knitro","text":"","category":"section"},{"location":"cops/","page":"COPS","title":"COPS","text":"name nvar ncon status objective opt_val time (s) #f #c dual_feas feas\nIsometrization of α-pinene 505 500 max_time 0.00e+00 1.99e+01 4.33e+00 1 1 0.00e+00 5.00e+01\nIsometrization of α-pinene 1005 1000 max_time 0.00e+00 1.99e+01 1.10e+00 1 1 0.00e+00 5.00e+01\nIsometrization of α-pinene 2005 2000 max_time 0.00e+00 1.99e+01 1.26e+00 1 1 0.00e+00 5.00e+01\nJournal Bearing 2600 0 max_time 1.20e+01 -1.55e-01 9.39e+00 1 0 5.88e-01 0.00e+00\nJournal Bearing 5775 0 max_time 5.06e+00 -1.55e-01 5.31e+00 2 0 2.31e-01 0.00e+00\nJournal Bearing 10200 0 max_time -1.05e+00 -1.55e-01 1.09e+00 5 0 3.17e-04 0.00e+00\nCatalyst Mixing 602 402 max_time 0.00e+00 -4.81e-02 2.82e+00 2 2 1.00e-02 2.49e-01\nCatalyst Mixing 1202 802 max_time 0.00e+00 -4.81e-02 2.56e+00 2 2 5.00e-03 2.49e-01\nCatalyst Mixing 2402 1602 max_time 0.00e+00 -4.81e-02 3.60e+00 2 2 2.50e-03 2.50e-01\nFlow in a Channel 800 800 first_order 0.00e+00 1.00e+00 5.12e+01 2 2 0.00e+00 1.99e-13\nFlow in a Channel 1600 1600 first_order 0.00e+00 1.00e+00 1.58e+00 2 2 0.00e+00 4.44e-16\nFlow in a Channel 3200 3200 first_order 0.00e+00 1.00e+00 1.55e+00 2 2 0.00e+00 6.66e-16\nTransition States for the Dirichlet Problem 9 0 first_order 0.00e+00 1.94e-06 5.16e-02 1 0 0.00e+00 0.00e+00\nTransition States for the Dirichlet Problem 19 0 first_order 0.00e+00 1.71e-02 1.99e-01 1 0 0.00e+00 0.00e+00\nTransition States for the Dirichlet Problem 39 0 first_order 0.00e+00 3.29e-02 4.02e-02 1 0 0.00e+00 0.00e+00\nCatalytic Cracking of Gas Oil 205 202 max_time 7.94e-02 5.24e-03 5.73e+01 2 2 7.01e-03 4.86e-07\nCatalytic Cracking of Gas Oil 405 402 max_time 7.93e-02 5.24e-03 1.45e+00 2 2 5.73e-03 3.20e-07\nCatalytic Cracking of Gas Oil 805 802 max_time 4.65e-02 5.24e-03 2.88e+00 2 2 3.14e-03 7.89e-05\nHang Glider 698 498 max_time -9.50e+02 1.25e+03 2.77e+01 1 1 4.44e-16 9.73e+00\nHang Glider 1398 998 max_time -9.50e+02 1.25e+03 2.74e+01 1 1 6.66e-16 4.86e+00\nHang Glider 2798 1998 max_time -9.50e+02 1.25e+03 2.77e+01 1 1 6.66e-16 2.43e+00\nTransition States for the Henon Problem 9 0 first_order 0.00e+00 7.22e+00 2.82e-02 1 0 0.00e+00 0.00e+00\nTransition States for the Henon Problem 19 0 first_order 0.00e+00 7.52e+01 2.74e-02 1 0 0.00e+00 0.00e+00\nTransition States for the Henon Problem 39 0 first_order 0.00e+00 1.26e+02 5.00e-02 1 0 0.00e+00 0.00e+00\nTransition States for the Lane-Emden Problem 9 0 first_order 0.00e+00 8.49e+00 2.56e-02 1 0 0.00e+00 0.00e+00\nTransition States for the Lane-Emden Problem 19 0 first_order 0.00e+00 9.11e+00 4.14e-02 1 0 0.00e+00 0.00e+00\nTransition States for the Lane-Emden Problem 39 0 first_order 0.00e+00 9.28e+00 3.79e-02 1 0 0.00e+00 0.00e+00\nMethanol to Hydrocarbons 308 303 exception 2.33e-01 9.02e-03 6.73e-01 1 1 1.80e+308 0.00e+00\nMethanol to Hydrocarbons 608 603 exception 2.33e-01 9.02e-03 5.03e-01 1 1 1.80e+308 0.00e+00\nMethanol to Hydrocarbons 1208 1203 exception 2.33e-01 9.02e-03 6.91e-01 1 1 1.80e+308 0.00e+00\nMinimal Surface with Obstacle 5002 2401 max_time 5.78e+00 2.51e+00 1.86e+01 3 3 5.09e-02 4.30e-04\nMinimal Surface with Obstacle 11252 5476 max_time 6.40e+00 2.51e+00 1.70e+00 3 3 3.33e-02 1.85e-04\nMinimal Surface with Obstacle 20002 9801 max_time 8.47e+00 2.51e+00 2.43e+00 3 3 2.65e-02 1.23e-04\nRobot Arm 1200 597 max_time 0.00e+00 9.14e+00 2.04e+00 2 2 0.00e+00 8.31e+03\nRobot Arm 2400 1197 max_time 0.00e+00 9.14e+00 1.79e+00 2 2 0.00e+00 1.66e+04\nRobot Arm 4800 2397 max_time 0.00e+00 9.14e+00 2.33e+00 2 2 0.00e+00 3.32e+04\nGoddard Rocket 2400 1600 max_time -1.00e+00 1.01e+00 3.13e+00 3 3 2.50e-03 4.61e-02\nGoddard Rocket 4800 3200 max_time -1.00e+00 1.01e+00 3.16e+00 3 3 1.25e-03 2.30e-02\nGoddard Rocket 9600 6400 max_time -1.00e+00 1.01e+00 3.36e+00 3 3 6.25e-04 1.15e-02\nParticle Steering 800 400 first_order 0.00e+00 5.55e-01 1.80e+01 2 2 0.00e+00 7.62e-12\nParticle Steering 1600 800 first_order 0.00e+00 5.55e-01 3.54e-01 2 2 0.00e+00 1.66e-11\nParticle Steering 3200 1600 first_order 0.00e+00 5.55e-01 5.49e-01 2 2 0.00e+00 2.86e-11\nElastic-Plastic Torsion 7802 7802 max_time 0.00e+00 -4.18e-01 1.93e+00 2 2 8.06e-04 5.92e-04\nElastic-Plastic Torsion 17327 17327 max_time 0.00e+00 -4.18e-01 1.19e+01 2 2 3.60e-04 2.64e-04\nElastic-Plastic Torsion 30602 30602 max_time 0.00e+00 -4.18e-01 2.72e+01 2 2 2.14e-04 1.49e-04","category":"page"},{"location":"cops/#ipopt","page":"COPS","title":"ipopt","text":"","category":"section"},{"location":"cops/","page":"COPS","title":"COPS","text":"name nvar ncon status objective opt_val time (s) #f #c dual_feas feas\nIsometrization of α-pinene 505 500 max_time 0.00e+00 1.99e+01 1.67e+00 1 1 0.00e+00 5.00e+01\nIsometrization of α-pinene 1005 1000 max_time 0.00e+00 1.99e+01 1.83e+00 1 1 0.00e+00 5.00e+01\nIsometrization of α-pinene 2005 2000 max_time 0.00e+00 1.99e+01 2.02e+00 1 1 0.00e+00 5.00e+01\nJournal Bearing 2600 0 max_time 0.00e+00 -1.55e-01 1.06e+00 9 0 2.19e-05 0.00e+00\nJournal Bearing 5775 0 max_time 0.00e+00 -1.55e-01 1.08e+00 4 0 5.14e-02 0.00e+00\nJournal Bearing 10200 0 max_time 0.00e+00 -1.55e-01 1.07e+00 3 0 1.74e-01 0.00e+00\nCatalyst Mixing 602 402 max_time 0.00e+00 -4.81e-02 2.58e+00 1 1 1.00e-02 2.50e-01\nCatalyst Mixing 1202 802 max_time 0.00e+00 -4.81e-02 2.53e+00 1 1 5.00e-03 2.50e-01\nCatalyst Mixing 2402 1602 max_time 0.00e+00 -4.81e-02 5.93e+00 1 1 2.50e-03 2.50e-01\nFlow in a Channel 800 800 max_time 0.00e+00 1.00e+00 2.68e+01 2 2 2.00e-02 3.32e-08\nFlow in a Channel 1600 1600 max_time 0.00e+00 1.00e+00 1.52e+00 2 2 2.00e-02 6.64e-08\nFlow in a Channel 3200 3200 max_time 0.00e+00 1.00e+00 1.15e+00 2 2 2.00e-02 1.33e-07\nTransition States for the Dirichlet Problem 9 0 first_order 0.00e+00 1.94e-06 4.90e-02 1 0 0.00e+00 0.00e+00\nTransition States for the Dirichlet Problem 19 0 first_order 0.00e+00 1.71e-02 1.48e-01 1 0 0.00e+00 0.00e+00\nTransition States for the Dirichlet Problem 39 0 first_order 0.00e+00 3.29e-02 4.40e-02 1 0 0.00e+00 0.00e+00\nCatalytic Cracking of Gas Oil 205 202 max_time 0.00e+00 5.24e-03 2.90e+00 2 2 1.03e-02 5.89e-06\nCatalytic Cracking of Gas Oil 405 402 max_time 0.00e+00 5.24e-03 1.42e+00 2 2 1.47e-02 3.88e-06\nCatalytic Cracking of Gas Oil 805 802 max_time 0.00e+00 5.24e-03 1.88e+00 2 2 3.79e-02 1.84e-06\nHang Glider 698 498 max_time 0.00e+00 1.25e+03 3.71e+01 1 1 1.00e+00 9.73e+00\nHang Glider 1398 998 max_time 0.00e+00 1.25e+03 3.77e+01 1 1 1.00e+00 4.86e+00\nHang Glider 2798 1998 max_time 0.00e+00 1.25e+03 3.86e+01 1 1 1.00e+00 2.43e+00\nTransition States for the Henon Problem 9 0 first_order 0.00e+00 7.22e+00 3.60e-02 1 0 0.00e+00 0.00e+00\nTransition States for the Henon Problem 19 0 first_order 0.00e+00 7.52e+01 4.00e-02 1 0 0.00e+00 0.00e+00\nTransition States for the Henon Problem 39 0 first_order 0.00e+00 1.26e+02 1.36e-01 1 0 0.00e+00 0.00e+00\nTransition States for the Lane-Emden Problem 9 0 first_order 0.00e+00 8.49e+00 3.80e-02 1 0 0.00e+00 0.00e+00\nTransition States for the Lane-Emden Problem 19 0 first_order 0.00e+00 9.11e+00 4.00e-02 1 0 0.00e+00 0.00e+00\nTransition States for the Lane-Emden Problem 39 0 first_order 0.00e+00 9.28e+00 3.90e-02 1 0 0.00e+00 0.00e+00\nMethanol to Hydrocarbons 308 303 unknown 0.00e+00 9.02e-03 1.67e+01 0 1 Inf Inf\nMethanol to Hydrocarbons 608 603 unknown 0.00e+00 9.02e-03 1.20e+00 0 1 Inf Inf\nMethanol to Hydrocarbons 1208 1203 unknown 0.00e+00 9.02e-03 1.03e+01 0 1 Inf Inf\nMinimal Surface with Obstacle 5002 2401 max_time 0.00e+00 2.51e+00 1.29e+00 1 1 1.00e+00 3.84e-04\nMinimal Surface with Obstacle 11252 5476 max_time 0.00e+00 2.51e+00 1.14e+01 1 1 1.00e+00 1.74e-04\nMinimal Surface with Obstacle 20002 9801 max_time 0.00e+00 2.51e+00 4.18e+01 1 1 1.00e+00 9.85e-05\nRobot Arm 1200 597 max_time 0.00e+00 9.14e+00 2.07e+00 1 1 0.00e+00 1.41e+04\nRobot Arm 2400 1197 max_time 0.00e+00 9.14e+00 2.08e+00 1 1 0.00e+00 2.83e+04\nRobot Arm 4800 2397 max_time 0.00e+00 9.14e+00 1.83e+00 1 1 0.00e+00 5.66e+04\nGoddard Rocket 2400 1600 max_time 0.00e+00 1.01e+00 2.92e+00 1 1 1.19e+00 1.00e-02\nGoddard Rocket 4800 3200 max_time 0.00e+00 1.01e+00 2.92e+00 1 1 1.00e+00 1.00e-02\nGoddard Rocket 9600 6400 max_time 0.00e+00 1.01e+00 2.36e+00 1 1 1.00e+00 1.00e-02\nParticle Steering 800 400 max_time 0.00e+00 5.55e-01 1.03e+01 2 2 0.00e+00 7.62e-12\nParticle Steering 1600 800 max_time 0.00e+00 5.55e-01 1.06e+00 4 4 0.00e+00 6.15e-12\nParticle Steering 3200 1600 max_time 0.00e+00 5.55e-01 1.07e+00 4 4 0.00e+00 5.94e-12\nElastic-Plastic Torsion 7802 7802 max_time 0.00e+00 -4.18e-01 7.97e+01 2 2 2.00e-07 1.01e-05\nElastic-Plastic Torsion 17327 17327 max_time 0.00e+00 -4.18e-01 3.60e+02 2 2 2.00e-07 5.46e-06\nElastic-Plastic Torsion 30602 30602 max_time 0.00e+00 -4.18e-01 1.14e+00 1 1 1.00e+00 5.05e-05","category":"page"},{"location":"","page":"Home","title":"Home","text":"CurrentModule = PDEOptimizationProblems","category":"page"},{"location":"#PDEOptimizationProblems","page":"Home","title":"PDEOptimizationProblems","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Documentation for PDEOptimizationProblems.","category":"page"}]
+}
diff --git a/previews/PR41/siteinfo.js b/previews/PR41/siteinfo.js
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--- /dev/null
+++ b/previews/PR41/siteinfo.js
@@ -0,0 +1 @@
+var DOCUMENTER_CURRENT_VERSION = "previews/PR41";
diff --git a/previews/PR41/tuto_rocket/index.html b/previews/PR41/tuto_rocket/index.html
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+<!DOCTYPE html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Rocket Control · PDEOptimizationProblems</title><script data-outdated-warner src="../assets/warner.js"></script><link rel="canonical" href="https://tmigot.github.io/PDEOptimizationProblems/tuto_rocket/"/><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script><link href="../assets/style.css" rel="stylesheet" type="text/css"/></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../"><img src="../assets/logo.png" alt="PDEOptimizationProblems logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../">PDEOptimizationProblems</a></span></div><form class="docs-search" action="../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><a class="tocitem" href="../cops/">COPS</a></li><li class="is-active"><a class="tocitem" href>Rocket Control</a><ul class="internal"><li><a class="tocitem" href="#Goddard-Rocket-Control"><span>Goddard Rocket Control</span></a></li></ul></li><li><a class="tocitem" href="../reference/">Reference</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Rocket Control</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Rocket Control</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/tmigot/PDEOptimizationProblems/blob/main/docs/src/tuto_rocket.md#" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h2 id="Goddard-Rocket-Control"><a class="docs-heading-anchor" href="#Goddard-Rocket-Control">Goddard Rocket Control</a><a id="Goddard-Rocket-Control-1"></a><a class="docs-heading-anchor-permalink" href="#Goddard-Rocket-Control" title="Permalink"></a></h2><pre><code class="language-julia hljs">using Gridap, PDENLPModels, PDEOptimizationProblems</code></pre><p>This tutorial shows how to solve a nonlinear rocketry control problem.  The problem was drawn from the <a href="https://www.mcs.anl.gov/~more/cops/cops3.pdf">COPS3</a> benchmark, and was used in <a href="https://jump.dev/JuMP.jl/stable/tutorials/Nonlinear%20programs/rocket_control/">JuMP&#39;s tutorials rocket control</a>.</p><p><code>PDEOptimizationProblems</code> contains a list of predefined PDE-constrained optimization problems, e.g. Goddard rocket control problem via the function <code>rocket</code>. Note that the models in <code>PDEOptimizationProblems</code> are in Lagrangian form, so the implementation considers a Mayer to Lagrange formulation that adds an additional (constant) function <code>H := h(T)</code> see <a href="https://github.com/tmigot/PDEOptimizationProblems/blob/main/src/rocket.jl">in the code</a>.</p><pre><code class="language-julia hljs">T = 0.2 # final time
+n = 800 # number of cells
+
+nlp = rocket(n = n, T = T)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">GridapPDENLPModel
+  Problem name: Goddard Rocket n=800
+   All variables: ████████████████████ 4800   All constraints: ████████████████████ 3200  
+            free: ████⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 801               free: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
+           lower: ███████⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 1600             lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
+           upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
+         low/upp: ██████████⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 2399           low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
+           fixed: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                fixed: ████████████████████ 3200  
+          infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
+            nnzh: ( 99.24% sparsity)   87971           linear: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
+                                                    nonlinear: ████████████████████ 3200  
+                                                         nnzj: ( 99.58% sparsity)   64001 
+
+  Counters:
+             obj: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                 grad: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                 cons: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
+        cons_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0             cons_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                 jcon: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
+           jgrad: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                  jac: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0              jac_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
+         jac_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                jprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0            jprod_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
+       jprod_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               jtprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0           jtprod_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
+      jtprod_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                 hess: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                hprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
+           jhess: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               jhprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
+</code></pre><p>The return model is a <code>GridapPDENLPModel</code> and, in particular, is an instance of an <code>AbstractNLPModel</code> that can be solved with any tool from the <a href="https://juliasmoothoptimizers.github.io/">JuliaSmoothOptimizers organization</a>. Then, using <a href="https://github.com/JuliaSmoothOptimizers/NLPModelsIpopt.jl">NLPModelsIpopt.jl</a>, we solve the model and get the required information.</p><pre><code class="language-julia hljs">using NLPModelsIpopt
+
+stats = ipopt(nlp, x0 = nlp.meta.x0)
+obj_ipopt, con_ipopt = stats.objective, stats.primal_feas
+(hh, Hh, vh, mh), uh = split_vectors(nlp, stats.solution)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(Base.Generator{UnitRange{Int64}, PDENLPModels.var&quot;#26#32&quot;{Vector{Float64}, Gridap.MultiField.MultiFieldFESpace{Gridap.MultiField.ConsecutiveMultiFieldStyle, Gridap.FESpaces.UnConstrained, Vector{Float64}}, PDENLPModels.var&quot;#sum_old#30&quot;, PDENLPModels.var&quot;#leng#28&quot;}}(PDENLPModels.var&quot;#26#32&quot;{Vector{Float64}, Gridap.MultiField.MultiFieldFESpace{Gridap.MultiField.ConsecutiveMultiFieldStyle, Gridap.FESpaces.UnConstrained, Vector{Float64}}, PDENLPModels.var&quot;#sum_old#30&quot;, PDENLPModels.var&quot;#leng#28&quot;}([1.0000000782063823, 1.0000003130096415, 1.0000007047709742, 1.0000012538374403, 1.0000019605418038, 1.0000028252023891, 1.0000038481229483, 1.000005029592539, 1.0000063698854187, 1.0000078692609484  …  0.000297218028758686, 0.000297218028758686, 0.0003279979227687755, 0.0003279979227687755, 0.0003276886489833575, 0.0003276886489833575, 0.0004048727303939331, 0.0004048727303939331, 0.00040439001850874984, 0.00040439001850874984], MultiFieldFESpace(), PDENLPModels.var&quot;#sum_old#30&quot;(), PDENLPModels.var&quot;#leng#28&quot;()), 1:4), [3.499593124492011, 3.499593124492011, 3.499583233072741, 3.499583233072741, 3.4995730612885647, 3.4995730612885647, 3.499562551364897, 3.499562551364897, 3.4995516768785424, 3.4995516768785424  …  0.000297218028758686, 0.000297218028758686, 0.0003279979227687755, 0.0003279979227687755, 0.0003276886489833575, 0.0003276886489833575, 0.0004048727303939331, 0.0004048727303939331, 0.00040439001850874984, 0.00040439001850874984])</code></pre><p>Finally, we can plot the functions, and the results match JuMP&#39;s tutorial and COPS 3 report.</p><pre><code class="language-julia hljs">using Plots
+gr()
+
+h₀, m₀, mᵪ = 1.0, 1.0, 0.6
+p = Plots.plot(
+  Plots.plot(0:T/n:T, vcat(h₀, hh); xlabel = &quot;Time (s)&quot;, ylabel = &quot;Altitude&quot;),
+  Plots.plot(0:T/n:T, vcat(m₀, mh, mᵪ * m₀); xlabel = &quot;Time (s)&quot;, ylabel = &quot;Mass&quot;),
+  Plots.plot(0:T/n:T, vcat(0., vh); xlabel = &quot;Time (s)&quot;, ylabel = &quot;Velocity&quot;),
+  Plots.plot(0:T/(length(uh) - 1):T, uh; xlabel = &quot;Time (s)&quot;, ylabel = &quot;Thrust&quot;),
+  layout = (2, 2),
+  legend = false,
+  margin = 1Plots.cm,
+)</code></pre><?xml version="1.0" encoding="utf-8"?>
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1815.13,1051 1815.49,1051 1815.86,1050.61 1816.23,1050.61 1816.59,1050.37 1816.96,1050.37 1817.33,1050.3 1817.69,1050.3 1818.06,1050.45 1818.42,1050.45 1818.79,1050.89 1819.16,1050.89 1819.52,1051.73 1819.89,1051.73 1820.26,1053.1 1820.62,1053.1 1820.99,1055.22 1821.35,1055.22 1821.72,1058.45 1822.09,1058.45 1822.45,1063.45 1822.82,1063.45 1823.19,1071.43 1823.55,1071.43 1823.92,1085.04 1824.28,1085.04 1824.65,1110.05 1825.02,1110.05 1825.38,1153.48 1825.75,1153.48 1826.12,1199.67 1826.48,1199.67 1826.85,1228.72 1827.21,1228.72 1827.58,1244.6 1827.95,1244.6 1828.31,1253.66 1828.68,1253.66 1829.05,1259.13 1829.41,1259.13 1829.78,1262.65 1830.14,1262.65 1830.51,1265.01 1830.88,1265.01 1831.24,1266.67 1831.61,1266.67 1831.98,1267.88 1832.34,1267.88 1832.71,1268.78 1833.07,1268.78 1833.44,1269.46 1833.81,1269.46 1834.17,1270.01 1834.54,1270.01 1834.91,1270.43 1835.27,1270.43 1835.64,1270.78 1836,1270.78 1836.37,1271.06 1836.74,1271.06 1837.1,1271.3 1837.47,1271.3 1837.84,1271.5 1838.2,1271.5 1838.57,1271.66 1838.93,1271.66 1839.3,1271.81 1839.67,1271.81 1840.03,1271.93 1840.4,1271.93 1840.77,1272.04 1841.13,1272.04 1841.5,1272.13 1841.86,1272.13 1842.23,1272.21 1842.6,1272.21 1842.96,1272.29 1843.33,1272.29 1843.7,1272.35 1844.06,1272.35 1844.43,1272.41 1844.79,1272.41 1845.16,1272.46 1845.53,1272.46 1845.89,1272.5 1846.26,1272.5 1846.62,1272.55 1846.99,1272.55 1847.36,1272.58 1847.72,1272.58 1848.09,1272.62 1848.46,1272.62 1848.82,1272.65 1849.19,1272.65 1849.55,1272.68 1849.92,1272.68 1850.29,1272.7 1850.65,1272.7 1851.02,1272.73 1851.39,1272.73 1851.75,1272.75 1852.12,1272.75 1852.48,1272.77 1852.85,1272.77 1853.22,1272.79 1853.58,1272.79 1853.95,1272.81 1854.32,1272.81 1854.68,1272.82 1855.05,1272.82 1855.41,1272.84 1855.78,1272.84 1856.15,1272.85 1856.51,1272.85 1856.88,1272.87 1857.25,1272.87 1857.61,1272.88 1857.98,1272.88 1858.34,1272.89 1858.71,1272.89 1859.08,1272.9 1859.44,1272.9 1859.81,1272.91 1860.18,1272.91 1860.54,1272.92 1860.91,1272.92 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2113.98,1273.17 2114.35,1273.17 2114.71,1273.17 2115.08,1273.17 2115.45,1273.17 2115.81,1273.17 2116.18,1273.17 2116.54,1273.17 2116.91,1273.17 2117.28,1273.17 2117.64,1273.17 2118.01,1273.17 2118.38,1273.17 2118.74,1273.17 2119.11,1273.17 2119.47,1273.17 2119.84,1273.17 2120.21,1273.17 2120.57,1273.17 2120.94,1273.17 2121.31,1273.17 2121.67,1273.17 2122.04,1273.17 2122.4,1273.17 2122.77,1273.17 2123.14,1273.17 2123.5,1273.17 2123.87,1273.17 2124.24,1273.17 2124.6,1273.17 2124.97,1273.17 2125.33,1273.17 2125.7,1273.17 2126.07,1273.17 2126.43,1273.17 2126.8,1273.17 2127.17,1273.17 2127.53,1273.17 2127.9,1273.17 2128.26,1273.17 2128.63,1273.17 2129,1273.17 2129.36,1273.17 2129.73,1273.17 2130.1,1273.17 2130.46,1273.17 2130.83,1273.17 2131.19,1273.17 2131.56,1273.17 2131.93,1273.17 2132.29,1273.17 2132.66,1273.17 2133.03,1273.17 2133.39,1273.17 2133.76,1273.17 2134.12,1273.17 2134.49,1273.17 2134.86,1273.17 2135.22,1273.17 2135.59,1273.17 2135.96,1273.17 2136.32,1273.17 2136.69,1273.17 2137.05,1273.17 2137.42,1273.17 2137.79,1273.17 2138.15,1273.17 2138.52,1273.17 2138.89,1273.17 2139.25,1273.17 2139.62,1273.17 2139.98,1273.17 2140.35,1273.17 2140.72,1273.17 2141.08,1273.17 2141.45,1273.17 2141.82,1273.17 2142.18,1273.17 2142.55,1273.17 2142.91,1273.17 2143.28,1273.17 2143.65,1273.17 2144.01,1273.17 2144.38,1273.17 2144.75,1273.17 2145.11,1273.17 2145.48,1273.17 2145.84,1273.17 2146.21,1273.17 2146.58,1273.17 2146.94,1273.17 2147.31,1273.17 2147.67,1273.17 2148.04,1273.17 2148.41,1273.17 2148.77,1273.17 2149.14,1273.17 2149.51,1273.17 2149.87,1273.17 2150.24,1273.17 2150.6,1273.17 2150.97,1273.17 2151.34,1273.17 2151.7,1273.17 2152.07,1273.17 2152.44,1273.17 2152.8,1273.17 2153.17,1273.17 2153.53,1273.17 2153.9,1273.17 2154.27,1273.17 2154.63,1273.17 2155,1273.17 2155.37,1273.17 2155.73,1273.17 2156.1,1273.17 2156.46,1273.17 2156.83,1273.17 2157.2,1273.17 2157.56,1273.17 2157.93,1273.17 2158.3,1273.17 2158.66,1273.17 2159.03,1273.17 2159.39,1273.17 2159.76,1273.17 2160.13,1273.17 2160.49,1273.17 2160.86,1273.17 2161.23,1273.17 2161.59,1273.17 2161.96,1273.17 2162.32,1273.17 2162.69,1273.17 2163.06,1273.17 2163.42,1273.17 2163.79,1273.17 2164.16,1273.17 2164.52,1273.17 2164.89,1273.17 2165.25,1273.17 2165.62,1273.17 2165.99,1273.17 2166.35,1273.17 2166.72,1273.17 2167.09,1273.17 2167.45,1273.17 2167.82,1273.17 2168.18,1273.17 2168.55,1273.17 2168.92,1273.17 2169.28,1273.17 2169.65,1273.17 2170.02,1273.17 2170.38,1273.17 2170.75,1273.17 2171.11,1273.17 2171.48,1273.17 2171.85,1273.17 2172.21,1273.17 2172.58,1273.17 2172.95,1273.17 2173.31,1273.17 2173.68,1273.17 2174.04,1273.17 2174.41,1273.17 2174.78,1273.17 2175.14,1273.17 2175.51,1273.17 2175.88,1273.17 2176.24,1273.17 2176.61,1273.17 2176.97,1273.17 2177.34,1273.17 2177.71,1273.17 2178.07,1273.17 2178.44,1273.17 2178.81,1273.17 2179.17,1273.17 2179.54,1273.17 2179.9,1273.17 2180.27,1273.17 2180.64,1273.17 2181,1273.17 2181.37,1273.17 2181.74,1273.17 2182.1,1273.17 2182.47,1273.17 2182.83,1273.17 2183.2,1273.17 2183.57,1273.17 2183.93,1273.17 2184.3,1273.17 2184.67,1273.17 2185.03,1273.17 2185.4,1273.17 2185.76,1273.17 2186.13,1273.17 2186.5,1273.17 2186.86,1273.17 2187.23,1273.17 2187.6,1273.17 2187.96,1273.16 2188.33,1273.16 2188.69,1273.16 2189.06,1273.16 2189.43,1273.16 2189.79,1273.16 2190.16,1273.16 2190.53,1273.16 2190.89,1273.16 2191.26,1273.16 2191.62,1273.16 2191.99,1273.16 2192.36,1273.15 2192.72,1273.15 2193.09,1273.15 2193.46,1273.15 "/>
+</svg>
+<p>An alternative is also to intepolate the entire solution over the domain as an <code>FEFunction</code> (Gridap&#39;s function type) and save the interpolation in a VTK file.</p><pre><code class="language-julia hljs">Ypde = nlp.pdemeta.Ypde
+h_h  = FEFunction(Ypde.spaces[1], hh)
+H_h  = FEFunction(Ypde.spaces[2], Hh)
+v_h  = FEFunction(Ypde.spaces[3], vh)
+m_h  = FEFunction(Ypde.spaces[4], mh)
+u_h  = FEFunction(nlp.pdemeta.Ycon, uh)
+
+writevtk(
+  nlp.pdemeta.tnrj.trian,
+  &quot;results_robot&quot;,
+  cellfields=[&quot;uh&quot; =&gt; u_h, &quot;hh&quot; =&gt; h_h, &quot;Hh&quot; =&gt; H_h, &quot;vh&quot; =&gt; v_h, &quot;mh&quot; =&gt; m_h],
+)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">([&quot;results_robot.vtu&quot;],)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../cops/">« COPS</a><a class="docs-footer-nextpage" href="../reference/">Reference »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Saturday 2 March 2024 22:37">Saturday 2 March 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>