OneServer.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "15a077c8-1466-4fc5-b100-d8a4b682ef91",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[33mWARNING: Skipping /opt/conda/lib/python3.11/site-packages/nlopt-2.7.1.dist-info due to invalid metadata entry 'name'\u001b[0m\u001b[33m\n",
      "\u001b[0mRequirement already satisfied: cvxpy in /home/jupyter/.local/lib/python3.11/site-packages (1.5.3)\n",
      "Requirement already satisfied: osqp>=0.6.2 in /home/jupyter/.local/lib/python3.11/site-packages (from cvxpy) (0.6.7.post1)\n",
      "Requirement already satisfied: ecos>=2 in /home/jupyter/.local/lib/python3.11/site-packages (from cvxpy) (2.0.14)\n",
      "Requirement already satisfied: clarabel>=0.5.0 in /home/jupyter/.local/lib/python3.11/site-packages (from cvxpy) (0.9.0)\n",
      "Requirement already satisfied: scs>=3.2.4.post1 in /home/jupyter/.local/lib/python3.11/site-packages (from cvxpy) (3.2.6)\n",
      "Requirement already satisfied: numpy>=1.15 in /opt/conda/lib/python3.11/site-packages (from cvxpy) (1.26.2)\n",
      "Requirement already satisfied: scipy>=1.1.0 in /opt/conda/lib/python3.11/site-packages (from cvxpy) (1.11.4)\n",
      "Requirement already satisfied: qdldl in /home/jupyter/.local/lib/python3.11/site-packages (from osqp>=0.6.2->cvxpy) (0.1.7.post4)\n",
      "\u001b[33mWARNING: Skipping /opt/conda/lib/python3.11/site-packages/nlopt-2.7.1.dist-info due to invalid metadata entry 'name'\u001b[0m\u001b[33m\n",
      "\u001b[0mNote: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip install cvxpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9f04a260-ccb0-4a10-84af-c5d734f59d69",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import cvxpy as cp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b5ba99e6-9671-4c0f-bb5a-021aa6a3114f",
   "metadata": {},
   "outputs": [],
   "source": [
    "#coords = np.random.randint(0, 100, size=(50,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7e83ced1-2d9f-4693-acdd-deb7dfa2be66",
   "metadata": {},
   "outputs": [],
   "source": [
    "# the user dataset\n",
    "coords = np.array([[76, 8], [77, 98], [75, 95], [22, 74], [79, 76], [61, 16], [66, 93], [ 9, 14], [ 2, 62], [63, 48], [ 6, 97], [12, 94], [48, 84], [26, 10], [74, 41], [83, 10], [47, 49], [36, 11], [47, 91], [36, 77], [56, 28], [18, 23], [22, 86], [76, 81], [ 8, 39], [21, 88], [88, 17], [ 4, 20], [83, 76], [ 5, 80], [41, 61], [72, 70], [22, 85], [30, 41], [34, 97], [66, 1], [ 9, 52], [97, 66], [73, 76], [66, 27], [54, 62], [56, 62], [ 2, 90], [45, 76], [29, 64], [43, 48], [20, 96], [15, 4], [20, 47], [78, 61]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f5664aeb-07b4-4f1e-a3ef-9f6883d3a906",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# display the user dataset\n",
    "plt.scatter(coords[:,0], coords[:,1])\n",
    "ax = plt.gca()\n",
    "ax.set_aspect('equal', adjustable='box')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ec4efe65-e69a-4170-a86f-87b7f1fc3214",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1890.8766374861061"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the optimal server location, using cvxpy\n",
    "x = cp.Variable((1, 2))\n",
    "obj = cp.Minimize(cp.sum(cp.norm(coords - x, 2, axis=1)))\n",
    "problem = cp.Problem(obj)\n",
    "problem.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "57e89f75-20a7-4515-a204-baef60632c45",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Variable((1, 2), var1)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# this is the coordinate of the optimal server location using cvxpy\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b1be3816-9589-4dad-9573-c2083e8ae916",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the solution\n",
    "plt.scatter(coords[:,0], coords[:,1])\n",
    "plt.scatter(x.value[:,0], x.value[:,1], color='red')\n",
    "ax = plt.gca()\n",
    "ax.set_aspect('equal', adjustable='box')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ce9271a8-16ee-4e10-96dc-737839ed4eed",
   "metadata": {},
   "outputs": [],
   "source": [
    "# the objective function at x\n",
    "def obj(x):\n",
    "    return np.sum(np.linalg.norm(x - coords) ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e7f8d81a-0bcb-4d23-ae99-04ade42c1726",
   "metadata": {},
   "outputs": [],
   "source": [
    "# the gradient of the objective function at x\n",
    "def grad(x):\n",
    "    return np.array([np.sum(2*(x[0]-coords[:,0])), np.sum(2*(x[1]-coords[:,1]))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "135e7872-4f46-40dc-afcd-f57fec9bdaf4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# gradient descent\n",
    "x = coords[0]\n",
    "steps = []\n",
    "ep = 1e-6\n",
    "beta = 0.7\n",
    "alpha = 0.3\n",
    "while np.linalg.norm(grad(x)) > ep:\n",
    "    steps.append(x)\n",
    "    del_x = -grad(x)\n",
    "    # use backtracking line search to find best t (step size)\n",
    "    t = 1\n",
    "    while obj(x + t*del_x) > (obj(x) - (t * alpha) * np.linalg.norm(del_x)**2):\n",
    "        t = beta * t\n",
    "    x = x + t * del_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ed41f884-d1cb-4ea8-85fa-9ec42f4ef044",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([43.95999999, 57.44000001])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# this is the coordinate of the optimal server location using cvxpy\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "60370e2a-c0fd-4666-b9dc-3347a4a4d19b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# the plot of gradient descent approaching the optimum\n",
    "gdFigure, gdAx = plt.subplots()\n",
    "gdAx.scatter(coords[:,0], coords[:,1])\n",
    "steps = np.array(steps)\n",
    "gdAx.plot(steps[:,0], steps[:,1], marker='s', color='black')\n",
    "gdAx.plot(x[0], x[1], marker='*', color='red')\n",
    "gdAx.set_aspect('equal', adjustable='box')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ad10b485-2acf-4583-b38e-5be8cf27a04c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "892"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get number of iterations\n",
    "steps.size"
   ]
  },
  {
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