From 177a0b29f6ac24f6ab0296b3afa3f51a27283daf Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Sat, 2 Mar 2024 23:48:18 +0000 Subject: [PATCH] build based on e7ef8ba --- dev/cops/index.html | 2 +- dev/index.html | 2 +- dev/reference/index.html | 2 +- dev/results_robot.vtu | Bin 120751 -> 120751 bytes dev/search/index.html | 2 +- dev/tuto_rocket/index.html | 210 ++++++++++++++++++------------------- 6 files changed, 109 insertions(+), 109 deletions(-) diff --git a/dev/cops/index.html b/dev/cops/index.html index 296f0fa..1027024 100644 --- a/dev/cops/index.html +++ b/dev/cops/index.html @@ -1,2 +1,2 @@ -COPS · PDEOptimizationProblems
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Simulations on COPS 3 test set

We run DCISolver.jl and NLPModelsIpopt.jl and NLPModelsKnitro.jl on an infinite-dimensional implementation of test problems from COPS 3.0 test set.

DCILDL

namenvarnconstatusobjectiveopt_valtime (s)#f#cdual_feasfeas
Isometrization of α-pinene505500max_time0.00e+001.99e+018.49e+00220.00e+002.84e+01
Isometrization of α-pinene10051000max_time0.00e+001.99e+014.05e+00220.00e+002.84e+01
Isometrization of α-pinene20052000max_time0.00e+001.99e+014.42e+00220.00e+002.84e+01
Journal Bearing26000exceptionInf-1.55e-01Inf00InfInf
Journal Bearing57750exceptionInf-1.55e-01Inf00InfInf
Journal Bearing102000exceptionInf-1.55e-01Inf00InfInf
Catalyst Mixing602402max_time0.00e+00-4.81e-029.96e+01111.41e-012.50e-01
Catalyst Mixing1202802max_time0.00e+00-4.81e-023.94e+00119.98e-022.50e-01
Catalyst Mixing24021602max_time0.00e+00-4.81e-021.07e+03227.07e-022.50e-01
Flow in a Channel800800max_time0.00e+001.00e+005.14e+00220.00e+002.20e-01
Flow in a Channel16001600max_time0.00e+001.00e+002.57e+00220.00e+002.20e-01
Flow in a Channel32003200max_time0.00e+001.00e+002.78e+00220.00e+002.20e-01
Transition States for the Dirichlet Problem90first_order0.00e+001.94e-060.00e+00110.00e+000.00e+00
Transition States for the Dirichlet Problem190first_order0.00e+001.71e-020.00e+00110.00e+000.00e+00
Transition States for the Dirichlet Problem390first_order0.00e+003.29e-020.00e+00110.00e+000.00e+00
Catalytic Cracking of Gas Oil205202max_time8.21e-025.24e-036.83e+01114.19e-020.00e+00
Catalytic Cracking of Gas Oil405402max_time8.11e-025.24e-031.11e+00112.97e-020.00e+00
Catalytic Cracking of Gas Oil805802max_time8.11e-025.24e-032.21e+00112.10e-020.00e+00
Hang Glider698498max_time-9.50e+021.25e+034.51e+03224.75e-158.79e+01
Hang Glider1398998max_time-9.50e+021.25e+038.86e+03226.76e-156.44e+01
Hang Glider27981998max_time-9.50e+021.25e+031.77e+04225.05e-094.66e+01
Transition States for the Henon Problem90first_order0.00e+007.22e+000.00e+00110.00e+000.00e+00
Transition States for the Henon Problem190first_order0.00e+007.52e+010.00e+00110.00e+000.00e+00
Transition States for the Henon Problem390first_order0.00e+001.26e+020.00e+00110.00e+000.00e+00
Transition States for the Lane-Emden Problem90first_order0.00e+008.49e+000.00e+00110.00e+000.00e+00
Transition States for the Lane-Emden Problem190first_order0.00e+009.11e+000.00e+00110.00e+000.00e+00
Transition States for the Lane-Emden Problem390first_order0.00e+009.28e+000.00e+00110.00e+000.00e+00
Methanol to Hydrocarbons308303exceptionInf9.02e-03Inf00InfInf
Methanol to Hydrocarbons608603exceptionInf9.02e-03Inf00InfInf
Methanol to Hydrocarbons12081203exceptionInf9.02e-03Inf00InfInf
Minimal Surface with Obstacle50022401max_time2.33e+002.51e+001.94e+01116.85e-027.34e-03
Minimal Surface with Obstacle112525476max_time2.32e+002.51e+001.59e+00225.29e-025.08e-03
Minimal Surface with Obstacle200029801max_time2.33e+002.51e+002.33e+00224.44e-023.84e-03
Robot Arm1200597max_time0.00e+009.14e+003.74e+00220.00e+002.01e+04
Robot Arm24001197max_time0.00e+009.14e+003.87e+00220.00e+004.02e+04
Robot Arm48002397max_time0.00e+009.14e+004.08e+00220.00e+008.04e+04
Goddard Rocket24001600max_time-1.00e+001.01e+004.83e+04221.85e-022.64e-01
Goddard Rocket48003200max_time-1.00e+001.01e+005.78e+04221.32e-021.90e-01
Goddard Rocket96006400max_time-1.00e+001.01e+001.23e+05229.39e-031.69e-01
Particle Steering800400max_time0.00e+005.55e-015.91e+01220.00e+001.35e+01
Particle Steering1600800max_time0.00e+005.55e-011.80e+02220.00e+009.56e+00
Particle Steering32001600max_time0.00e+005.55e-016.38e+02220.00e+006.79e+00
Elastic-Plastic Torsion78027802max_time0.00e+00-4.18e-015.58e+01115.72e-029.93e-03
Elastic-Plastic Torsion1732717327max_time0.00e+00-4.18e-012.22e+00113.82e-026.64e-03
Elastic-Plastic Torsion3060230602max_time0.00e+00-4.18e-012.71e+00112.87e-024.98e-03

knitro

namenvarnconstatusobjectiveopt_valtime (s)#f#cdual_feasfeas
Isometrization of α-pinene505500max_time0.00e+001.99e+014.33e+00110.00e+005.00e+01
Isometrization of α-pinene10051000max_time0.00e+001.99e+011.10e+00110.00e+005.00e+01
Isometrization of α-pinene20052000max_time0.00e+001.99e+011.26e+00110.00e+005.00e+01
Journal Bearing26000max_time1.20e+01-1.55e-019.39e+00105.88e-010.00e+00
Journal Bearing57750max_time5.06e+00-1.55e-015.31e+00202.31e-010.00e+00
Journal Bearing102000max_time-1.05e+00-1.55e-011.09e+00503.17e-040.00e+00
Catalyst Mixing602402max_time0.00e+00-4.81e-022.82e+00221.00e-022.49e-01
Catalyst Mixing1202802max_time0.00e+00-4.81e-022.56e+00225.00e-032.49e-01
Catalyst Mixing24021602max_time0.00e+00-4.81e-023.60e+00222.50e-032.50e-01
Flow in a Channel800800first_order0.00e+001.00e+005.12e+01220.00e+001.99e-13
Flow in a Channel16001600first_order0.00e+001.00e+001.58e+00220.00e+004.44e-16
Flow in a Channel32003200first_order0.00e+001.00e+001.55e+00220.00e+006.66e-16
Transition States for the Dirichlet Problem90first_order0.00e+001.94e-065.16e-02100.00e+000.00e+00
Transition States for the Dirichlet Problem190first_order0.00e+001.71e-021.99e-01100.00e+000.00e+00
Transition States for the Dirichlet Problem390first_order0.00e+003.29e-024.02e-02100.00e+000.00e+00
Catalytic Cracking of Gas Oil205202max_time7.94e-025.24e-035.73e+01227.01e-034.86e-07
Catalytic Cracking of Gas Oil405402max_time7.93e-025.24e-031.45e+00225.73e-033.20e-07
Catalytic Cracking of Gas Oil805802max_time4.65e-025.24e-032.88e+00223.14e-037.89e-05
Hang Glider698498max_time-9.50e+021.25e+032.77e+01114.44e-169.73e+00
Hang Glider1398998max_time-9.50e+021.25e+032.74e+01116.66e-164.86e+00
Hang Glider27981998max_time-9.50e+021.25e+032.77e+01116.66e-162.43e+00
Transition States for the Henon Problem90first_order0.00e+007.22e+002.82e-02100.00e+000.00e+00
Transition States for the Henon Problem190first_order0.00e+007.52e+012.74e-02100.00e+000.00e+00
Transition States for the Henon Problem390first_order0.00e+001.26e+025.00e-02100.00e+000.00e+00
Transition States for the Lane-Emden Problem90first_order0.00e+008.49e+002.56e-02100.00e+000.00e+00
Transition States for the Lane-Emden Problem190first_order0.00e+009.11e+004.14e-02100.00e+000.00e+00
Transition States for the Lane-Emden Problem390first_order0.00e+009.28e+003.79e-02100.00e+000.00e+00
Methanol to Hydrocarbons308303exception2.33e-019.02e-036.73e-01111.80e+3080.00e+00
Methanol to Hydrocarbons608603exception2.33e-019.02e-035.03e-01111.80e+3080.00e+00
Methanol to Hydrocarbons12081203exception2.33e-019.02e-036.91e-01111.80e+3080.00e+00
Minimal Surface with Obstacle50022401max_time5.78e+002.51e+001.86e+01335.09e-024.30e-04
Minimal Surface with Obstacle112525476max_time6.40e+002.51e+001.70e+00333.33e-021.85e-04
Minimal Surface with Obstacle200029801max_time8.47e+002.51e+002.43e+00332.65e-021.23e-04
Robot Arm1200597max_time0.00e+009.14e+002.04e+00220.00e+008.31e+03
Robot Arm24001197max_time0.00e+009.14e+001.79e+00220.00e+001.66e+04
Robot Arm48002397max_time0.00e+009.14e+002.33e+00220.00e+003.32e+04
Goddard Rocket24001600max_time-1.00e+001.01e+003.13e+00332.50e-034.61e-02
Goddard Rocket48003200max_time-1.00e+001.01e+003.16e+00331.25e-032.30e-02
Goddard Rocket96006400max_time-1.00e+001.01e+003.36e+00336.25e-041.15e-02
Particle Steering800400first_order0.00e+005.55e-011.80e+01220.00e+007.62e-12
Particle Steering1600800first_order0.00e+005.55e-013.54e-01220.00e+001.66e-11
Particle Steering32001600first_order0.00e+005.55e-015.49e-01220.00e+002.86e-11
Elastic-Plastic Torsion78027802max_time0.00e+00-4.18e-011.93e+00228.06e-045.92e-04
Elastic-Plastic Torsion1732717327max_time0.00e+00-4.18e-011.19e+01223.60e-042.64e-04
Elastic-Plastic Torsion3060230602max_time0.00e+00-4.18e-012.72e+01222.14e-041.49e-04

ipopt

namenvarnconstatusobjectiveopt_valtime (s)#f#cdual_feasfeas
Isometrization of α-pinene505500max_time0.00e+001.99e+011.67e+00110.00e+005.00e+01
Isometrization of α-pinene10051000max_time0.00e+001.99e+011.83e+00110.00e+005.00e+01
Isometrization of α-pinene20052000max_time0.00e+001.99e+012.02e+00110.00e+005.00e+01
Journal Bearing26000max_time0.00e+00-1.55e-011.06e+00902.19e-050.00e+00
Journal Bearing57750max_time0.00e+00-1.55e-011.08e+00405.14e-020.00e+00
Journal Bearing102000max_time0.00e+00-1.55e-011.07e+00301.74e-010.00e+00
Catalyst Mixing602402max_time0.00e+00-4.81e-022.58e+00111.00e-022.50e-01
Catalyst Mixing1202802max_time0.00e+00-4.81e-022.53e+00115.00e-032.50e-01
Catalyst Mixing24021602max_time0.00e+00-4.81e-025.93e+00112.50e-032.50e-01
Flow in a Channel800800max_time0.00e+001.00e+002.68e+01222.00e-023.32e-08
Flow in a Channel16001600max_time0.00e+001.00e+001.52e+00222.00e-026.64e-08
Flow in a Channel32003200max_time0.00e+001.00e+001.15e+00222.00e-021.33e-07
Transition States for the Dirichlet Problem90first_order0.00e+001.94e-064.90e-02100.00e+000.00e+00
Transition States for the Dirichlet Problem190first_order0.00e+001.71e-021.48e-01100.00e+000.00e+00
Transition States for the Dirichlet Problem390first_order0.00e+003.29e-024.40e-02100.00e+000.00e+00
Catalytic Cracking of Gas Oil205202max_time0.00e+005.24e-032.90e+00221.03e-025.89e-06
Catalytic Cracking of Gas Oil405402max_time0.00e+005.24e-031.42e+00221.47e-023.88e-06
Catalytic Cracking of Gas Oil805802max_time0.00e+005.24e-031.88e+00223.79e-021.84e-06
Hang Glider698498max_time0.00e+001.25e+033.71e+01111.00e+009.73e+00
Hang Glider1398998max_time0.00e+001.25e+033.77e+01111.00e+004.86e+00
Hang Glider27981998max_time0.00e+001.25e+033.86e+01111.00e+002.43e+00
Transition States for the Henon Problem90first_order0.00e+007.22e+003.60e-02100.00e+000.00e+00
Transition States for the Henon Problem190first_order0.00e+007.52e+014.00e-02100.00e+000.00e+00
Transition States for the Henon Problem390first_order0.00e+001.26e+021.36e-01100.00e+000.00e+00
Transition States for the Lane-Emden Problem90first_order0.00e+008.49e+003.80e-02100.00e+000.00e+00
Transition States for the Lane-Emden Problem190first_order0.00e+009.11e+004.00e-02100.00e+000.00e+00
Transition States for the Lane-Emden Problem390first_order0.00e+009.28e+003.90e-02100.00e+000.00e+00
Methanol to Hydrocarbons308303unknown0.00e+009.02e-031.67e+0101InfInf
Methanol to Hydrocarbons608603unknown0.00e+009.02e-031.20e+0001InfInf
Methanol to Hydrocarbons12081203unknown0.00e+009.02e-031.03e+0101InfInf
Minimal Surface with Obstacle50022401max_time0.00e+002.51e+001.29e+00111.00e+003.84e-04
Minimal Surface with Obstacle112525476max_time0.00e+002.51e+001.14e+01111.00e+001.74e-04
Minimal Surface with Obstacle200029801max_time0.00e+002.51e+004.18e+01111.00e+009.85e-05
Robot Arm1200597max_time0.00e+009.14e+002.07e+00110.00e+001.41e+04
Robot Arm24001197max_time0.00e+009.14e+002.08e+00110.00e+002.83e+04
Robot Arm48002397max_time0.00e+009.14e+001.83e+00110.00e+005.66e+04
Goddard Rocket24001600max_time0.00e+001.01e+002.92e+00111.19e+001.00e-02
Goddard Rocket48003200max_time0.00e+001.01e+002.92e+00111.00e+001.00e-02
Goddard Rocket96006400max_time0.00e+001.01e+002.36e+00111.00e+001.00e-02
Particle Steering800400max_time0.00e+005.55e-011.03e+01220.00e+007.62e-12
Particle Steering1600800max_time0.00e+005.55e-011.06e+00440.00e+006.15e-12
Particle Steering32001600max_time0.00e+005.55e-011.07e+00440.00e+005.94e-12
Elastic-Plastic Torsion78027802max_time0.00e+00-4.18e-017.97e+01222.00e-071.01e-05
Elastic-Plastic Torsion1732717327max_time0.00e+00-4.18e-013.60e+02222.00e-075.46e-06
Elastic-Plastic Torsion3060230602max_time0.00e+00-4.18e-011.14e+00111.00e+005.05e-05
+COPS · PDEOptimizationProblems
Edit on GitHub

Simulations on COPS 3 test set

We run DCISolver.jl and NLPModelsIpopt.jl and NLPModelsKnitro.jl on an infinite-dimensional implementation of test problems from COPS 3.0 test set.

DCILDL

namenvarnconstatusobjectiveopt_valtime (s)#f#cdual_feasfeas
Isometrization of α-pinene505500max_time0.00e+001.99e+018.49e+00220.00e+002.84e+01
Isometrization of α-pinene10051000max_time0.00e+001.99e+014.05e+00220.00e+002.84e+01
Isometrization of α-pinene20052000max_time0.00e+001.99e+014.42e+00220.00e+002.84e+01
Journal Bearing26000exceptionInf-1.55e-01Inf00InfInf
Journal Bearing57750exceptionInf-1.55e-01Inf00InfInf
Journal Bearing102000exceptionInf-1.55e-01Inf00InfInf
Catalyst Mixing602402max_time0.00e+00-4.81e-029.96e+01111.41e-012.50e-01
Catalyst Mixing1202802max_time0.00e+00-4.81e-023.94e+00119.98e-022.50e-01
Catalyst Mixing24021602max_time0.00e+00-4.81e-021.07e+03227.07e-022.50e-01
Flow in a Channel800800max_time0.00e+001.00e+005.14e+00220.00e+002.20e-01
Flow in a Channel16001600max_time0.00e+001.00e+002.57e+00220.00e+002.20e-01
Flow in a Channel32003200max_time0.00e+001.00e+002.78e+00220.00e+002.20e-01
Transition States for the Dirichlet Problem90first_order0.00e+001.94e-060.00e+00110.00e+000.00e+00
Transition States for the Dirichlet Problem190first_order0.00e+001.71e-020.00e+00110.00e+000.00e+00
Transition States for the Dirichlet Problem390first_order0.00e+003.29e-020.00e+00110.00e+000.00e+00
Catalytic Cracking of Gas Oil205202max_time8.21e-025.24e-036.83e+01114.19e-020.00e+00
Catalytic Cracking of Gas Oil405402max_time8.11e-025.24e-031.11e+00112.97e-020.00e+00
Catalytic Cracking of Gas Oil805802max_time8.11e-025.24e-032.21e+00112.10e-020.00e+00
Hang Glider698498max_time-9.50e+021.25e+034.51e+03224.75e-158.79e+01
Hang Glider1398998max_time-9.50e+021.25e+038.86e+03226.76e-156.44e+01
Hang Glider27981998max_time-9.50e+021.25e+031.77e+04225.05e-094.66e+01
Transition States for the Henon Problem90first_order0.00e+007.22e+000.00e+00110.00e+000.00e+00
Transition States for the Henon Problem190first_order0.00e+007.52e+010.00e+00110.00e+000.00e+00
Transition States for the Henon Problem390first_order0.00e+001.26e+020.00e+00110.00e+000.00e+00
Transition States for the Lane-Emden Problem90first_order0.00e+008.49e+000.00e+00110.00e+000.00e+00
Transition States for the Lane-Emden Problem190first_order0.00e+009.11e+000.00e+00110.00e+000.00e+00
Transition States for the Lane-Emden Problem390first_order0.00e+009.28e+000.00e+00110.00e+000.00e+00
Methanol to Hydrocarbons308303exceptionInf9.02e-03Inf00InfInf
Methanol to Hydrocarbons608603exceptionInf9.02e-03Inf00InfInf
Methanol to Hydrocarbons12081203exceptionInf9.02e-03Inf00InfInf
Minimal Surface with Obstacle50022401max_time2.33e+002.51e+001.94e+01116.85e-027.34e-03
Minimal Surface with Obstacle112525476max_time2.32e+002.51e+001.59e+00225.29e-025.08e-03
Minimal Surface with Obstacle200029801max_time2.33e+002.51e+002.33e+00224.44e-023.84e-03
Robot Arm1200597max_time0.00e+009.14e+003.74e+00220.00e+002.01e+04
Robot Arm24001197max_time0.00e+009.14e+003.87e+00220.00e+004.02e+04
Robot Arm48002397max_time0.00e+009.14e+004.08e+00220.00e+008.04e+04
Goddard Rocket24001600max_time-1.00e+001.01e+004.83e+04221.85e-022.64e-01
Goddard Rocket48003200max_time-1.00e+001.01e+005.78e+04221.32e-021.90e-01
Goddard Rocket96006400max_time-1.00e+001.01e+001.23e+05229.39e-031.69e-01
Particle Steering800400max_time0.00e+005.55e-015.91e+01220.00e+001.35e+01
Particle Steering1600800max_time0.00e+005.55e-011.80e+02220.00e+009.56e+00
Particle Steering32001600max_time0.00e+005.55e-016.38e+02220.00e+006.79e+00
Elastic-Plastic Torsion78027802max_time0.00e+00-4.18e-015.58e+01115.72e-029.93e-03
Elastic-Plastic Torsion1732717327max_time0.00e+00-4.18e-012.22e+00113.82e-026.64e-03
Elastic-Plastic Torsion3060230602max_time0.00e+00-4.18e-012.71e+00112.87e-024.98e-03

knitro

namenvarnconstatusobjectiveopt_valtime (s)#f#cdual_feasfeas
Isometrization of α-pinene505500max_time0.00e+001.99e+014.33e+00110.00e+005.00e+01
Isometrization of α-pinene10051000max_time0.00e+001.99e+011.10e+00110.00e+005.00e+01
Isometrization of α-pinene20052000max_time0.00e+001.99e+011.26e+00110.00e+005.00e+01
Journal Bearing26000max_time1.20e+01-1.55e-019.39e+00105.88e-010.00e+00
Journal Bearing57750max_time5.06e+00-1.55e-015.31e+00202.31e-010.00e+00
Journal Bearing102000max_time-1.05e+00-1.55e-011.09e+00503.17e-040.00e+00
Catalyst Mixing602402max_time0.00e+00-4.81e-022.82e+00221.00e-022.49e-01
Catalyst Mixing1202802max_time0.00e+00-4.81e-022.56e+00225.00e-032.49e-01
Catalyst Mixing24021602max_time0.00e+00-4.81e-023.60e+00222.50e-032.50e-01
Flow in a Channel800800first_order0.00e+001.00e+005.12e+01220.00e+001.99e-13
Flow in a Channel16001600first_order0.00e+001.00e+001.58e+00220.00e+004.44e-16
Flow in a Channel32003200first_order0.00e+001.00e+001.55e+00220.00e+006.66e-16
Transition States for the Dirichlet Problem90first_order0.00e+001.94e-065.16e-02100.00e+000.00e+00
Transition States for the Dirichlet Problem190first_order0.00e+001.71e-021.99e-01100.00e+000.00e+00
Transition States for the Dirichlet Problem390first_order0.00e+003.29e-024.02e-02100.00e+000.00e+00
Catalytic Cracking of Gas Oil205202max_time7.94e-025.24e-035.73e+01227.01e-034.86e-07
Catalytic Cracking of Gas Oil405402max_time7.93e-025.24e-031.45e+00225.73e-033.20e-07
Catalytic Cracking of Gas Oil805802max_time4.65e-025.24e-032.88e+00223.14e-037.89e-05
Hang Glider698498max_time-9.50e+021.25e+032.77e+01114.44e-169.73e+00
Hang Glider1398998max_time-9.50e+021.25e+032.74e+01116.66e-164.86e+00
Hang Glider27981998max_time-9.50e+021.25e+032.77e+01116.66e-162.43e+00
Transition States for the Henon Problem90first_order0.00e+007.22e+002.82e-02100.00e+000.00e+00
Transition States for the Henon Problem190first_order0.00e+007.52e+012.74e-02100.00e+000.00e+00
Transition States for the Henon Problem390first_order0.00e+001.26e+025.00e-02100.00e+000.00e+00
Transition States for the Lane-Emden Problem90first_order0.00e+008.49e+002.56e-02100.00e+000.00e+00
Transition States for the Lane-Emden Problem190first_order0.00e+009.11e+004.14e-02100.00e+000.00e+00
Transition States for the Lane-Emden Problem390first_order0.00e+009.28e+003.79e-02100.00e+000.00e+00
Methanol to Hydrocarbons308303exception2.33e-019.02e-036.73e-01111.80e+3080.00e+00
Methanol to Hydrocarbons608603exception2.33e-019.02e-035.03e-01111.80e+3080.00e+00
Methanol to Hydrocarbons12081203exception2.33e-019.02e-036.91e-01111.80e+3080.00e+00
Minimal Surface with Obstacle50022401max_time5.78e+002.51e+001.86e+01335.09e-024.30e-04
Minimal Surface with Obstacle112525476max_time6.40e+002.51e+001.70e+00333.33e-021.85e-04
Minimal Surface with Obstacle200029801max_time8.47e+002.51e+002.43e+00332.65e-021.23e-04
Robot Arm1200597max_time0.00e+009.14e+002.04e+00220.00e+008.31e+03
Robot Arm24001197max_time0.00e+009.14e+001.79e+00220.00e+001.66e+04
Robot Arm48002397max_time0.00e+009.14e+002.33e+00220.00e+003.32e+04
Goddard Rocket24001600max_time-1.00e+001.01e+003.13e+00332.50e-034.61e-02
Goddard Rocket48003200max_time-1.00e+001.01e+003.16e+00331.25e-032.30e-02
Goddard Rocket96006400max_time-1.00e+001.01e+003.36e+00336.25e-041.15e-02
Particle Steering800400first_order0.00e+005.55e-011.80e+01220.00e+007.62e-12
Particle Steering1600800first_order0.00e+005.55e-013.54e-01220.00e+001.66e-11
Particle Steering32001600first_order0.00e+005.55e-015.49e-01220.00e+002.86e-11
Elastic-Plastic Torsion78027802max_time0.00e+00-4.18e-011.93e+00228.06e-045.92e-04
Elastic-Plastic Torsion1732717327max_time0.00e+00-4.18e-011.19e+01223.60e-042.64e-04
Elastic-Plastic Torsion3060230602max_time0.00e+00-4.18e-012.72e+01222.14e-041.49e-04

ipopt

namenvarnconstatusobjectiveopt_valtime (s)#f#cdual_feasfeas
Isometrization of α-pinene505500max_time0.00e+001.99e+011.67e+00110.00e+005.00e+01
Isometrization of α-pinene10051000max_time0.00e+001.99e+011.83e+00110.00e+005.00e+01
Isometrization of α-pinene20052000max_time0.00e+001.99e+012.02e+00110.00e+005.00e+01
Journal Bearing26000max_time0.00e+00-1.55e-011.06e+00902.19e-050.00e+00
Journal Bearing57750max_time0.00e+00-1.55e-011.08e+00405.14e-020.00e+00
Journal Bearing102000max_time0.00e+00-1.55e-011.07e+00301.74e-010.00e+00
Catalyst Mixing602402max_time0.00e+00-4.81e-022.58e+00111.00e-022.50e-01
Catalyst Mixing1202802max_time0.00e+00-4.81e-022.53e+00115.00e-032.50e-01
Catalyst Mixing24021602max_time0.00e+00-4.81e-025.93e+00112.50e-032.50e-01
Flow in a Channel800800max_time0.00e+001.00e+002.68e+01222.00e-023.32e-08
Flow in a Channel16001600max_time0.00e+001.00e+001.52e+00222.00e-026.64e-08
Flow in a Channel32003200max_time0.00e+001.00e+001.15e+00222.00e-021.33e-07
Transition States for the Dirichlet Problem90first_order0.00e+001.94e-064.90e-02100.00e+000.00e+00
Transition States for the Dirichlet Problem190first_order0.00e+001.71e-021.48e-01100.00e+000.00e+00
Transition States for the Dirichlet Problem390first_order0.00e+003.29e-024.40e-02100.00e+000.00e+00
Catalytic Cracking of Gas Oil205202max_time0.00e+005.24e-032.90e+00221.03e-025.89e-06
Catalytic Cracking of Gas Oil405402max_time0.00e+005.24e-031.42e+00221.47e-023.88e-06
Catalytic Cracking of Gas Oil805802max_time0.00e+005.24e-031.88e+00223.79e-021.84e-06
Hang Glider698498max_time0.00e+001.25e+033.71e+01111.00e+009.73e+00
Hang Glider1398998max_time0.00e+001.25e+033.77e+01111.00e+004.86e+00
Hang Glider27981998max_time0.00e+001.25e+033.86e+01111.00e+002.43e+00
Transition States for the Henon Problem90first_order0.00e+007.22e+003.60e-02100.00e+000.00e+00
Transition States for the Henon Problem190first_order0.00e+007.52e+014.00e-02100.00e+000.00e+00
Transition States for the Henon Problem390first_order0.00e+001.26e+021.36e-01100.00e+000.00e+00
Transition States for the Lane-Emden Problem90first_order0.00e+008.49e+003.80e-02100.00e+000.00e+00
Transition States for the Lane-Emden Problem190first_order0.00e+009.11e+004.00e-02100.00e+000.00e+00
Transition States for the Lane-Emden Problem390first_order0.00e+009.28e+003.90e-02100.00e+000.00e+00
Methanol to Hydrocarbons308303unknown0.00e+009.02e-031.67e+0101InfInf
Methanol to Hydrocarbons608603unknown0.00e+009.02e-031.20e+0001InfInf
Methanol to Hydrocarbons12081203unknown0.00e+009.02e-031.03e+0101InfInf
Minimal Surface with Obstacle50022401max_time0.00e+002.51e+001.29e+00111.00e+003.84e-04
Minimal Surface with Obstacle112525476max_time0.00e+002.51e+001.14e+01111.00e+001.74e-04
Minimal Surface with Obstacle200029801max_time0.00e+002.51e+004.18e+01111.00e+009.85e-05
Robot Arm1200597max_time0.00e+009.14e+002.07e+00110.00e+001.41e+04
Robot Arm24001197max_time0.00e+009.14e+002.08e+00110.00e+002.83e+04
Robot Arm48002397max_time0.00e+009.14e+001.83e+00110.00e+005.66e+04
Goddard Rocket24001600max_time0.00e+001.01e+002.92e+00111.19e+001.00e-02
Goddard Rocket48003200max_time0.00e+001.01e+002.92e+00111.00e+001.00e-02
Goddard Rocket96006400max_time0.00e+001.01e+002.36e+00111.00e+001.00e-02
Particle Steering800400max_time0.00e+005.55e-011.03e+01220.00e+007.62e-12
Particle Steering1600800max_time0.00e+005.55e-011.06e+00440.00e+006.15e-12
Particle Steering32001600max_time0.00e+005.55e-011.07e+00440.00e+005.94e-12
Elastic-Plastic Torsion78027802max_time0.00e+00-4.18e-017.97e+01222.00e-071.01e-05
Elastic-Plastic Torsion1732717327max_time0.00e+00-4.18e-013.60e+02222.00e-075.46e-06
Elastic-Plastic Torsion3060230602max_time0.00e+00-4.18e-011.14e+00111.00e+005.05e-05
diff --git a/dev/index.html b/dev/index.html index 2352227..a85029f 100644 --- a/dev/index.html +++ b/dev/index.html @@ -1,2 +1,2 @@ -Home · PDEOptimizationProblems
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diff --git a/dev/reference/index.html b/dev/reference/index.html index 2f1175e..5f3a4f6 100644 --- a/dev/reference/index.html +++ b/dev/reference/index.html @@ -1,2 +1,2 @@ -Reference · PDEOptimizationProblems
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Reference

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Contents

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Index

​

​

PDEOptimizationProblems.meta — Constant
PDEOptimizationProblems.meta

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

  • domaindim: dimension of the domain 1/2/3 for 1D/2D/3D
  • pbtype: in pbtypes
  • nθ: size of the unknown vector
  • ny: number of unknown function
  • nu: number of control function

Solution meta

  • optimalvalue: best known objective value (NaN if unknown, -Inf if unbounded problem)

Classification

  • objtype: in objtypes
  • contype: in contypes
  • origin: in origins
  • has_cvx_obj: true if the problem has a convex objective
  • has_cvx_con: true if the problem has convex constraints
  • has_bounds: true if the problem has bound constraints
  • has_fixed_variables: true if it has fixed variables
source
PDEOptimizationProblems.burger1d — Method

Burger1d(;n :: Int = 512, kwargs...)

Let 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.

This 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.

The specificity of the problem:

  • quadratic objective function;
  • nonlinear constraints with AD jacobian;

Suggestions:

  • FEOperatorFromTerms has only one term. We might consider splitting linear and

nonlinear terms.

source
PDEOptimizationProblems.cellincrease — Method

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.

Using a photosynthetic rate proportional to the photosynthetic apparatus mass fraction.

source
PDEOptimizationProblems.cellincrease_MichaelisMenten — Method

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.

Using Michaelis-Menten's function for the photosynthetic rate.

source
PDEOptimizationProblems.controlelasticmembrane1 — Method

controlelasticmembrane1(; n :: Int = 10, args...)

Let Ω = (-1,1)^2, we solve the following distributed Poisson control problem with Dirichlet boundary:

min{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.

source
PDEOptimizationProblems.controlelasticmembrane2 — Method

controlelasticmembrane2(; n :: Int = 10, args...)

Let Ω = (-1,1)^2, we solve the following distributed Poisson control problem with Dirichlet boundary:

min{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.

source
PDEOptimizationProblems.incompressiblenavierstokes — Method

incompressibleNavierStokes(; n :: Int64 = 3, kargs...)

This corresponds to the incompressible Navier-Stokes equation described in the Gridap Tutorials: https://gridap.github.io/Tutorials/stable/pages/t008incnavier_stokes/

It has no objective function and no control, just the PDE.

source
PDEOptimizationProblems.inversepoissonproblem2d — Method

inversePoissonproblem2d(;n :: Int = 512, kwargs...)

Let 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)

This 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.

source
PDEOptimizationProblems.membrane — Method

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

The 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.

source
PDEOptimizationProblems.penalizedpoisson — Method

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.

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

This example has been used in Exercice 10.2.4 (p. 308) of G. Allaire, Analyse numérique et optimisation, Les éditions de Polytechnique

source
PDEOptimizationProblems.poisson3d — Method

poisson3d(; n :: Int = 10)

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.

It is inspired from the 2nd tutorial in Gridap.jl: https://gridap.github.io/Tutorials/stable/pages/t002_validation/

source
PDEOptimizationProblems.poissonboltzman2d — Method

poissonBoltzman2d(; n :: Int = 100)

Let 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

The 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.

This 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.

The specificity of the problem:

  • quadratic objective function;
  • nonlinear constraints with AD jacobian;
source
PDEOptimizationProblems.smallestlaplacianeigenvalue — Method

smallestLaplacianeigenvalue(; n :: Int = 10, args...)

We solve the following problem:

min{u,z} ∫Ω​ |∇u|^2 s.t. ∫_Ω​ u^2 = 1, for x ∈ Ω u = 0, for x ∈ ∂Ω

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

Δu + λ u = 0, for x ∈ Ω u = 0, for x ∈ ∂Ω

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

TODO:

  • does the 1 work as it is? or should it be put in lcon, ucon?
  • it is 1D for now.
source
+Reference · PDEOptimizationProblems
Edit on GitHub

Reference

​

Contents

​

​

Index

​

​

PDEOptimizationProblems.meta — Constant
PDEOptimizationProblems.meta

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

  • domaindim: dimension of the domain 1/2/3 for 1D/2D/3D
  • pbtype: in pbtypes
  • nθ: size of the unknown vector
  • ny: number of unknown function
  • nu: number of control function

Solution meta

  • optimalvalue: best known objective value (NaN if unknown, -Inf if unbounded problem)

Classification

  • objtype: in objtypes
  • contype: in contypes
  • origin: in origins
  • has_cvx_obj: true if the problem has a convex objective
  • has_cvx_con: true if the problem has convex constraints
  • has_bounds: true if the problem has bound constraints
  • has_fixed_variables: true if it has fixed variables
source
PDEOptimizationProblems.burger1d — Method

Burger1d(;n :: Int = 512, kwargs...)

Let 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.

This 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.

The specificity of the problem:

  • quadratic objective function;
  • nonlinear constraints with AD jacobian;

Suggestions:

  • FEOperatorFromTerms has only one term. We might consider splitting linear and

nonlinear terms.

source
PDEOptimizationProblems.cellincrease — Method

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.

Using a photosynthetic rate proportional to the photosynthetic apparatus mass fraction.

source
PDEOptimizationProblems.cellincrease_MichaelisMenten — Method

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.

Using Michaelis-Menten's function for the photosynthetic rate.

source
PDEOptimizationProblems.controlelasticmembrane1 — Method

controlelasticmembrane1(; n :: Int = 10, args...)

Let Ω = (-1,1)^2, we solve the following distributed Poisson control problem with Dirichlet boundary:

min{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.

source
PDEOptimizationProblems.controlelasticmembrane2 — Method

controlelasticmembrane2(; n :: Int = 10, args...)

Let Ω = (-1,1)^2, we solve the following distributed Poisson control problem with Dirichlet boundary:

min{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.

source
PDEOptimizationProblems.incompressiblenavierstokes — Method

incompressibleNavierStokes(; n :: Int64 = 3, kargs...)

This corresponds to the incompressible Navier-Stokes equation described in the Gridap Tutorials: https://gridap.github.io/Tutorials/stable/pages/t008incnavier_stokes/

It has no objective function and no control, just the PDE.

source
PDEOptimizationProblems.inversepoissonproblem2d — Method

inversePoissonproblem2d(;n :: Int = 512, kwargs...)

Let 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)

This 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.

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PDEOptimizationProblems.membrane — Method

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

The 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.

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PDEOptimizationProblems.penalizedpoisson — Method

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.

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

This example has been used in Exercice 10.2.4 (p. 308) of G. Allaire, Analyse numérique et optimisation, Les éditions de Polytechnique

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PDEOptimizationProblems.poisson3d — Method

poisson3d(; n :: Int = 10)

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.

It is inspired from the 2nd tutorial in Gridap.jl: https://gridap.github.io/Tutorials/stable/pages/t002_validation/

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PDEOptimizationProblems.poissonboltzman2d — Method

poissonBoltzman2d(; n :: Int = 100)

Let 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

The 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.

This 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.

The specificity of the problem:

  • quadratic objective function;
  • nonlinear constraints with AD jacobian;
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PDEOptimizationProblems.smallestlaplacianeigenvalue — Method

smallestLaplacianeigenvalue(; n :: Int = 10, args...)

We solve the following problem:

min{u,z} ∫Ω​ |∇u|^2 s.t. ∫_Ω​ u^2 = 1, for x ∈ Ω u = 0, for x ∈ ∂Ω

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

Δu + λ u = 0, for x ∈ Ω u = 0, for x ∈ ∂Ω

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

TODO:

  • does the 1 work as it is? or should it be put in lcon, ucon?
  • it is 1D for now.
source
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-1,2 +1,2 @@ -Search · PDEOptimizationProblems

Loading search...

    +Search · PDEOptimizationProblems

    Loading search...

      diff --git a/dev/tuto_rocket/index.html b/dev/tuto_rocket/index.html index 92e1f5e..c854693 100644 --- a/dev/tuto_rocket/index.html +++ b/dev/tuto_rocket/index.html @@ -27,7 +27,7 @@ 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)
      (Base.Generator{UnitRange{Int64}, PDENLPModels.var"#26#32"{Vector{Float64}, Gridap.MultiField.MultiFieldFESpace{Gridap.MultiField.ConsecutiveMultiFieldStyle, Gridap.FESpaces.UnConstrained, Vector{Float64}}, PDENLPModels.var"#sum_old#30", PDENLPModels.var"#leng#28"}}(PDENLPModels.var"#26#32"{Vector{Float64}, Gridap.MultiField.MultiFieldFESpace{Gridap.MultiField.ConsecutiveMultiFieldStyle, Gridap.FESpaces.UnConstrained, Vector{Float64}}, PDENLPModels.var"#sum_old#30", PDENLPModels.var"#leng#28"}([1.0000000782063823, 1.0000003130096415, 1.0000007047709742, 1.0000012538374403, 1.0000019605418038, 1.0000028252023891, 1.0000038481229483, 1.000005029592539, 1.0000063698854187, 1.0000078692609484  …  0.00029721802875868556, 0.00029721802875868556, 0.0003279979227687752, 0.0003279979227687752, 0.0003276886489833572, 0.0003276886489833572, 0.0004048727303939332, 0.0004048727303939332, 0.0004043900185087497, 0.0004043900185087497], MultiFieldFESpace(), PDENLPModels.var"#sum_old#30"(), PDENLPModels.var"#leng#28"()), 1:4), [3.499593124492011, 3.499593124492011, 3.499583233072741, 3.499583233072741, 3.4995730612885647, 3.4995730612885647, 3.499562551364897, 3.499562551364897, 3.4995516768785424, 3.4995516768785424  …  0.00029721802875868556, 0.00029721802875868556, 0.0003279979227687752, 0.0003279979227687752, 0.0003276886489833572, 0.0003276886489833572, 0.0004048727303939332, 0.0004048727303939332, 0.0004043900185087497, 0.0004043900185087497])

      Finally, we can plot the functions, and the results match JuMP's tutorial and COPS 3 report.

      using Plots
+(hh, Hh, vh, mh), uh = split_vectors(nlp, stats.solution)
      (Base.Generator{UnitRange{Int64}, PDENLPModels.var"#26#32"{Vector{Float64}, Gridap.MultiField.MultiFieldFESpace{Gridap.MultiField.ConsecutiveMultiFieldStyle, Gridap.FESpaces.UnConstrained, Vector{Float64}}, PDENLPModels.var"#sum_old#30", PDENLPModels.var"#leng#28"}}(PDENLPModels.var"#26#32"{Vector{Float64}, Gridap.MultiField.MultiFieldFESpace{Gridap.MultiField.ConsecutiveMultiFieldStyle, Gridap.FESpaces.UnConstrained, Vector{Float64}}, PDENLPModels.var"#sum_old#30", PDENLPModels.var"#leng#28"}([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"#sum_old#30"(), PDENLPModels.var"#leng#28"()), 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])

      Finally, we can plot the functions, and the results match JuMP's tutorial and COPS 3 report.

      using Plots
 gr()
 
 h₀, m₀, mᵪ = 1.0, 1.0, 0.6
@@ -42,132 +42,132 @@
 )
      - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + +

      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.

      Ypde = nlp.pdemeta.Ypde
 h_h  = FEFunction(Ypde.spaces[1], hh)
@@ -180,4 +180,4 @@
   nlp.pdemeta.tnrj.trian,
   "results_robot",
   cellfields=["uh" => u_h, "hh" => h_h, "Hh" => H_h, "vh" => v_h, "mh" => m_h],
-)
      (["results_robot.vtu"],)
      +)
      (["results_robot.vtu"],)