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This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters. Learn more about bidirectional Unicode charactersOriginal file line number Diff line number Diff line change @@ -0,0 +1,175 @@ { "metadata": { "name": "Assigment3q1" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "from cvxopt import solvers\n", "import numpy as np\n", "from cvxopt import matrix\n", "import pprint" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 32 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This question comes from assignment 3 q1 from here: https://class.coursera.org/linearprogramming-001/quiz/feedback?submission_id=262352 We will be trying to solve the following LP problem:\n", " \n", "$$Max~-x_0$$\n", "\n", "Given the following constraints:\n", "\n", "$$-1x_0-1x_1-1x_2-0x_3\\le5$$\n", "$$-1x_0+1x_1-2x_2+1x_3\\le-10$$\n", "$$-1x_0+1x_1+0x_2-1x_3\\le1-20$$\n", "$$-1x_0+1x_1+1x_2+1x_3\\le3$$\n", "$$x_0,x_1,x_2,x_3\\ge0$$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "c = matrix([[-1,0,0,0]],tc=\"d\") #coefficient of x0 is -1\n", "\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 62 }, { "cell_type": "code", "collapsed": false, "input": [ "\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 57 }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "A = matrix([[-1.,-1.,-1.,-1.,-1.,0.,0.,0.], [-1.,1., 1., 1.,0.,-1.,0.,0.],[-1.,-2.,0.,1., 0.,0.,-1.,0.],[0.,1.,-1.,1.,0.,0.,0.,-1.]],tc='d')\n", "print(A)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[-1.00e+00 -1.00e+00 -1.00e+00 0.00e+00]\n", "[-1.00e+00 1.00e+00 -2.00e+00 1.00e+00]\n", "[-1.00e+00 1.00e+00 0.00e+00 -1.00e+00]\n", "[-1.00e+00 1.00e+00 1.00e+00 1.00e+00]\n", "[-1.00e+00 0.00e+00 0.00e+00 0.00e+00]\n", "[ 0.00e+00 -1.00e+00 0.00e+00 0.00e+00]\n", "[ 0.00e+00 0.00e+00 -1.00e+00 0.00e+00]\n", "[ 0.00e+00 0.00e+00 0.00e+00 -1.00e+00]\n", "\n" ] } ], "prompt_number": 58 }, { "cell_type": "code", "collapsed": false, "input": [ "b = matrix([5, -10, -20, 3, 0, 0, 0, 0], tc='d')\n", "print b\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[ 5.00e+00]\n", "[-1.00e+01]\n", "[-2.00e+01]\n", "[ 3.00e+00]\n", "[ 0.00e+00]\n", "[ 0.00e+00]\n", "[ 0.00e+00]\n", "[ 0.00e+00]\n", "\n" ] } ], "prompt_number": 59 }, { "cell_type": "code", "collapsed": false, "input": [ "sol = solvers.lp(-c, A, b) #Maximize -x0\n", "print (sol['x'])" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " pcost dcost gap pres dres k/t\n", " 0: 1.6508e+00 2.5321e+01 8e+01 1e+00 6e+00 1e+00\n", " 1: 1.2018e+01 1.8145e+01 2e+01 2e-01 2e+00 8e-01\n", " 2: 1.1164e+01 1.1760e+01 1e+00 2e-02 1e-01 1e-01\n", " 3: 1.0672e+01 1.0681e+01 2e-02 3e-04 2e-03 2e-03\n", " 4: 1.0667e+01 1.0667e+01 2e-04 3e-06 2e-05 2e-05\n", " 5: 1.0667e+01 1.0667e+01 2e-06 3e-08 2e-07 2e-07\n", " 6: 1.0667e+01 1.0667e+01 2e-08 3e-10 2e-09 2e-09\n", "Optimal solution found.\n", "[ 1.07e+01]\n", "[-5.07e-10]\n", "[ 4.33e+00]\n", "[ 9.33e+00]\n", "\n" ] } ], "prompt_number": 65 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 37 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }