{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "# Problem Sheet 1 Part B - Solutions\n", "***\n", "$\\newcommand{\\vct}[1]{\\mathbf{#1}}$\n", "$\\newcommand{\\mtx}[1]{\\mathbf{#1}}$\n", "$\\newcommand{\\e}{\\varepsilon}$\n", "$\\newcommand{\\norm}[1]{\\|#1\\|}$\n", "$\\newcommand{\\minimize}{\\text{minimize}\\quad}$\n", "$\\newcommand{\\maximize}{\\text{maximize}\\quad}$\n", "$\\newcommand{\\subjto}{\\quad\\text{subject to}\\quad}$\n", "$\\newcommand{\\R}{\\mathbb{R}}$\n", "$\\newcommand{\\trans}{T}$\n", "$\\newcommand{\\ip}[2]{\\langle {#1}, {#2} \\rangle}$\n", "$\\newcommand{\\zerovct}{\\vct{0}}$\n", "$\\newcommand{\\diff}[1]{\\mathrm{d}{#1}}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution to Problem 1.5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(a) The unit circle with respect to the $\\infty$-norm is the square with corners $(\\pm 1,\\pm 1)^{\\trans}$.\n", "\n", "(b) The trick in transforming the unconstrained problem\n", "\n", "\\begin{equation*}\n", " \\minimize \\norm{\\mtx{A}\\vct{x}-\\vct{b}}_{\\infty}\n", "\\end{equation*}\n", "\n", "into a constrained linear programming problem is to characterise the $\\infty$-norm as the solution of a minimization problem. In fact, for any set of numbers $x_1,\\dots,x_n$,\n", "\n", "\\begin{equation*}\n", " \\max_{1\\leq i\\leq n} |x_i| = \\min_{\\forall i\\colon |x_i|\\leq t} t.\n", "\\end{equation*}\n", "\n", "Put simply, the *maximum* of a set of non-negative numbers is the *smallest* upper bound on these numbers. We can further replace the condition $|x_i|\\leq t$ by $-t\\leq x_i\\leq t$, so that the problem becomes\n", "\n", "\\begin{align*}\n", "\\mathop{\\text{minimize}}_{(\\vct{x},t)} \\quad & t \\\\\n", "\\subjto & -t \\leq \\vct{a}_1^{\\trans} \\vct{x} - b_1 \\leq t\\\\\n", "& \\cdots\\\\\n", "& -t \\leq \\vct{a}_m^{\\trans}\\vct{x} - b_m \\leq t,\n", "\\end{align*}\n", "\n", "where $\\mtx{a}_i^{\\trans}$ are the rows of the matrix $\\mtx{A}$. This problem can be brought into {\\em standard form} by replacing each condition with the pair of conditions\n", "\n", "\\begin{align*}\n", " \\vct{a}_i^{\\trans}\\vct{x}-t&\\leq b_i\\\\\n", " -\\vct{a}_i^{\\trans}\\vct{x}-t& \\leq -b_i.\n", "\\end{align*}\n", "\n", "The solution $\\vct{x}$ of this problem can be read off the solution $(\\vct{x},t)$ of the original problem." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution to Problem 1.6" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import numpy.linalg as la\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def graddesc(A, b, x, tol):\n", " # Compute the negative gradient r = A^T(b-Ax)\n", " r = np.dot(A.transpose(),b-np.dot(A,x))\n", " # Start with an empty array\n", " xout = [x]\n", " while la.norm(r,2) > tol:\n", " # If the gradient is bigger than the tolerance\n", " Ar = np.dot(A,r)\n", " alpha = np.dot(r,r)/np.dot(Ar,Ar)\n", " x = x + alpha*r\n", " xout.append(x)\n", " r = r-alpha*np.dot(A.transpose(),Ar)\n", " return np.array(xout).transpose()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "A = np.array([[1,2], [2,1], [-1,0]])\n", "b = np.array([10, -1, 0])\n", "tol = 1e-4\n", "x = np.zeros(2)\n", "\n", "traj = graddesc(A, b, x, tol)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXEAAAEACAYAAABF+UbAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xl8lOXZL/DflY3sCSRA2AIoIMGyiIi411qVuuHW9/S1\ndcEeq61tXU5btS6HuuBSFewpVqu+qK1oWysVrSIULG1BRLawJciegGQj+77Mff6YJTNJJpnl2ef3\n/XzyMZk8M3PlIfy4vZ77uW9RSoGIiOwpzuwCiIgocgxxIiIbY4gTEdkYQ5yIyMYY4kRENsYQJyKy\nsbBCXESyROQvIlIkIrtF5Ey9CiMiooElhHn8CwA+Ukp9W0QSAKTqUBMREYVIQr3ZR0QyAWxTSp2s\nb0lERBSqcNop4wFUichSEdkqIr8XkRS9CiMiooGFE+IJAGYCWKKUmgmgGcD9ulRFREQhCacnfhRA\nqVJqs+frdwHc53+AiHAhFiKiCCilJJLnhRziSqlyESkVkUlKqS8BXARgT8/jrr7zy0jqMFTRpt+g\nYPZPzS5jQKxTW5HWOWPOOO2L6cen7z2KC699xND3DJfWNc4siCi/BrTs5Udxw+3WPpcAcNWsxIif\nG+7slJ8CeEtEEgEcBDA/4nfW0epl16CpZnfAYzMvfh75k64wqSKys+0bDxse5LFma5HSLcidLqwQ\nV0oVAjhDp1o00VeAA8DW1feirbkKE2fcYnxRZHvbNx4GYPyoPJZsLXJ3Yxnm4XHcHZt9BbjX7vUL\n8dmHdyA9e7yBFUUud5Q97qWKpTq9Ya6ncQUX6P4e0dKzRm+Ya2Hq6dY/l9EKeZ54SC8moszuif9t\nyaQBj0nNzMc585YiLXOMARWRU3FUrr9YGZVfNStR/wubTtJcX4Kd/1mIhIRUtDZXIDl1GArm3M1Q\np7CwV64/9soH5rgQTxt8ar8tFa+Kkn/D1dXu+7q6vJCjcwobe+X6Y6+8f47riV98w3IkZ04Y8Dj/\nAAfco/OijYv1KosczoheeazTslfuJI4LcQCYe+NHuPjGNRiUOiys57U2V+hUEcWC7RsPM8x1trVI\nMcx7cGSIA0Ba5hicf93bSM3MD/k5yWGGPlFfGOT6Y5B3c1xP3F9a5hicM28pijYuRmtzBRqq96Ot\n5USfxyanDcfE0+/o9/Wa6kt9r8WLodQfXvTUH3vlbo6bYtifzav+D47u+6DX4/EJqUhJH4mWxqNI\nzRiFrNwCZOUWIDN3MrJyC5Ccmoum+lKsf38+mutLfM/jVEUKBcNcf3YP8mimGMZUiA8UxK6udjTU\nHERdVZHnoxh1VUWIi08CALQ1V/Z6zdETr8SsS54z7Gcge2KQG8OuYc4QD0O4LRGlFFoay/DZh7eh\nobr3z5Y76kyce/Uf9CyZHIRhrj87Bjlv9glDWuaYsEbOIoLUjBFISs7q8/u8GErhYK9cf7F2g5Bj\nZ6doqfLoZ6ir2ovktOEBj6dm5qNgzt0mVUV2xdkr+oulqYgxNxIPV3XZNnyx6h7MuexFpGSM4OwU\n0gTv9DRGLIzKY64nHgpv37yh9hAaqr/E9PMXYOyU680uixyKQW4MK4d5ND1xtlN68M5gObrvA9RV\n7oKrqx17t7yEpvpSs0sjh2J7xRhOba8wxHso2rg4YAoi4F5XZdvaX6K1qfcUQyIt8JZ9YzgxyNkT\n7yHY+im1lUVY8/bliItLQNbQAmR5bgTKyi1AetY4SFy8wZWSE3H2iv6cdqcnQ7yHYFMG88ZegNMv\nfhYtjWWoP+G+CeirA594LnRWITNnIrJyJnsCvgCZQyYhISnN4OrJCRjkxnDKRU9e2OwhktvrO9ob\nUe+5u9N7p2dDzX6kpI8IGLFn5RZgUOpQiNj/F4eMwTA3htlhzjs2NabFQleurg401h7y3brv/tgD\nSFxAqGflFiA9exzi4oL/TxEX3optDHJjmBnkDHGbUEqhtak8YF2WuqoitDZVIGPIBE+ou0fumTmn\nIDEpnQtvEQAGuVHMCnKGuM11tDei/sTegHBvqN6H5LThcHW1o6XxeK/ncOGt2MMgN47RYc61U2wu\nMSkdOSNOR86I032PuVydaKw9jE0rf9Lnc7gLUezhBU/j2OmiJ+eJW1RcXAIyh0wI2jLhwluxifPJ\njWOXOeUMcQtrqitBbcUuJKUMCXicC28Rg9wYdlhIi+0Ui2ppLMP6Fbdg8uwfY1j+eZydQr2wvWIc\nK7dXeGHTgtpaqvHv5Tdg7OTrMXHm/za7HLI4Brlx9ApywxbAEpHDIlIoIttEZFMkb0j9a2+rx4YV\n8zHy5LkMcAoJWyvGsWJrJdyeuAvA15VSpymlZutRUCzrbG/Cxg9vQ87I2SiYfZfZ5ZCNMMiNY7U+\nebghLhE8h0LQ1dmGzz/+EdIHn4yp5z7AW/MpbJy5YiyrBHm4gawArBaRL0TkNj0KikWurg588cld\nSErOxmlffwwi/HeSIscgN44VgjzctDhHKTUTwGUA7hSRc3WoKaYoVxe2rrkPSrlw+jd/zSVtSRMM\ncuOYHeRhTTFUSh33/LdSRJYDmA3gP/7HFG36je/z3FFnYuioMzUo05mUUti+7hG0NlfhrCt+j7j4\nJLNLIgfhFETjhLtG+c7N67BzyzpN3jvkKYYikgogTinVKCJpAFYB+JVSapXfMZxiGCKlFHatfxLV\nZdtw9lVLkZiUbnZJ5FAMcmNFMg3RqLVThgNYLiLK87y3/AOc+tdzOdnE5Gyc+GoTzr36jwxw0hVH\n5MYy+sagkENcKXUIwAwda3GsvpaTFUnAede9g6TkLBMro1jBIDeWkUHOaRAG6GvzZaU6cbDwDZMq\noljEi53GMmo+OUPcAMGWja0uL0Tl0Y1ob601uCKKVQxy4+kd5FwAywDBlo0ViUPxphdQV1WMxEFZ\nfjv7uHf3Sc0cw5t+SHNsrRhPz/YKF8AywEBbrCnlQnP9UdR6tmvzbrrc0d6ArBy/jZaHFiBjyETE\ncyoiaYBBbrxgQc7t2Wwgks2O21tremy0XIymuiNIyxqLrNzJyMyZjGxPuCclDzboJyEnYZAbr68g\nZ4jHkK7ONjTU7EddpSfYT7hDPjEpHZneEXtuAbJzC5CaOZq38NOAGOTG6xnkDPEYp5RCc8NRd6hX\ndm+23NFW5x6x+3rtBcgcMgnxCYPMLpkshkFuDm+YM8SpT+2ttT3aMUVoqjuC1Mwx3X12T7gP6rEF\nHMUeBrk5ZhYId7unviUlZ2Po6DkYOnqO77GurnY0VO/3hXvZ4U9RV1WEhMTUXsGelpXPdgyRzqKd\ngsiROHnaMccCRux1VcXoaK1FZs4pvlDPyi1AZs4kxCckm10y6YSjcXMsuDGJ7RTSXntrHepP7A0I\n98baQ0jNGB0wYs/KLcCg1ByzyyWNMMiNF02Is51CQSUlZyF31Gzkjureic/V1Y6GmgO+0Xr51n+h\nrqoI8fHJAaGeNbQAaVlj2Y6xId4MZC8ciVPUlFJoaTzeox1ThPaWGmTmTPK0YSb72jEJiSlml0wh\nYJAbhyNxMpWIIDVjJFIzRmLE+It8j7e31bvbMZVFqCkvxOHd76Cx9iBSMkb6XUR1fySn5pr4E1Bf\nOCK3B4Y46SZpUCZyR56B3JFn+B5zdXWgofagb077vq2voK6qGHHxiX7tGPd/07PGcbs6ogGwnUKm\nc7djynq1Y9qaTyAzZ2LAiN3djkkNeH4kSxpQ6Dga1x9np5AjdbQ3+hYD815IbajZj5T0Ed2zYlJy\nULx5CVoajvme57+4GGmDQa4vhjjFDFdXBxprD/mCvXTvCrS1VPU6bvTEKzHrkudMqNC5GOT64YVN\nihlx8YnIzJmEzJxJGHPKPNRW7kbbsd4hHmwjDiKn4SResrWEIJtMB9uIgyLHXYGsiSFOttXSVI6a\nit291lJPzcxHwZy7TarK2Rjk1sN2CtlSW0s1Nrw/HydPvQGjJl7O2SkUsxjiZDsdbQ3Y8MH3MWL8\nRZh0+h0AwIuYBuJNQNbCdgrZSmdHMz77+20YkncaCubca3Y5RKbTPMRnzBnHf6VJF11d7fj84zuR\nnjUO0857CCL67B5OA2Nv3Dp0G4l7w5yBTlpwdXVg8yd3IzEpAzMufJyrI1oAg9waDPmbwDCnaCjl\nwta1D8DV1Y5ZFz+LuDheyiHyMnQ4w9E5hUsphcJ1v0JLYxlmf+u3iItPMrsk8sPRuPlMG9J4g5y/\nBBSMUgq7NzyD2spdOGfeG9wWjqgPYY3ERSRORLaKyAqtCuDonILZu/lFVJT8G2df+RoSg9yZSebj\nQMxc4bZT7gKwR49CAPbOqdv+wtdRuvd9nH3VUiQlZ5tdDpFlhRziIjIawGUAXtWvHDeOzmPb4T1/\nwYHCN3DOvNeRnDbU7HKILC2ckfgiAD8HoN3atSFgoMeWo/v+juJNL+Ccq5YiNWOk2eVQiNhSMU9I\nFzZF5HIA5Uqp7SLydQBB77L49L1HfZ+PK7gA4wsuiLZGH14Mdbbjh9Zi57+fwNnzliI9e5zZ5RDp\n5lDROhwuWqfJa4W0KYSILATwPQCdAFIAZAB4Tyl1U4/j1II/tGtSWKgY6M5QefQzfLHqHpx1+csY\nPHy62eVQBPh/y5GLZlOIkNopSqlfKqXylVInAfgOgLU9A9wsbLfYX3XZNnyx6h7MvvQ3DHAb44DK\nHI66d5lhbj+1lXvw+Uc/wukXPYPcUbPNLofIdsK+2UcptQ6ANs0cnfgHOUcH1tVQcwAbP/wBpl2w\nAMPHnm92OUS25PhFKBjo1tRUfxQbVtyKKWfdi1EnX2p2OUS25ah2ykDYP7eGlqZybHj/FkyceRvy\nJ19rdjmkIQ6UjOf4kXgwHKGbw7ut2tgp38ZJU79ndjlEthezIe6PgW6MwG3Vbje7HCJHYIj3wEDX\nB7dVI9IHQ7wfDHRtcFs1Iv0wxEPEQI+My9XJbdWIdMQQjwADPTRKubB1zf1wdbXjzEsXc1s1Ih3w\nb1WUGOh9899W7ewrX+W2ajGC03eNxxDXEAPdTSmF3Z/9GnWVu3H2vNe5rRqRjhjiOuk5IomlUPdu\nq3bu1X/gtmpEOmOIGyRWRunebdXOu+YtbqtGZACGuAmcGujebdXOu+YtbqsWg9gPNwdD3GR2brs0\n1ZeiaONitDZXwNXVgcbawzj/une4rRqRgRjiFmOXUXpTfSnWvz8fzfUlvsdS0vMgcfEmVkVm4Sjc\nPAxxC7PyKL1o4+KAAAeAlsYyFG1cjFmXPGdSVUSxhyFuI1Yapbc2V/T5eE3FLlSXFSIzZxISElMM\nrorMwFG4uRjiNmX2KD05dVifjyvVicJ1j6Ch5iBSM0chK7cg4CM5NdfQOklfDHDzMcQdwuhQL5hz\nN6rLCwNaKqmZ+Thn3lKkZY6Bq6sdDTUHUVdVhLqqIuzb+grqqooQF5+ErNzJnlB3/zc9axx76UQR\nEqWUdi8mohb8oV2z1yPt6BHq/rNTklOHoWDO3UjLHBP0eKUUWhqP+4Ld/VGMtuYTyMyZGDBid7dj\nUjWvmbTDUbh2FtyYBKVURMt7MsRjlNk9dX8dbQ2oO1HsC/W6qiI01hxASvoIv2B3j9oHpQ7lUrYW\nwADXFkOcomalUAcAV1cHGmo97ZjK7lF7XFx8jz77ZKRnj2c7xkAMcO0xxElzVgt1wN2OaW0qD2zH\nVBahtbkSmUPc7ZhMb7895xQkJKWZXbKjMLz1E02I88Im9amvv7BmB7uIICU9Dynpecgbd6Hv8Y72\nRtR72jB1lbtRUvRXNNTsR3JaXkArJmtoAZJTh7EdEwEGuHUxxClkZk9rDCYxKR05I2chZ+Qs32Mu\nVycaaw75RuwHCl9HXdUeQOK6WzE5ntkxg8dzw4ogGN7Wx3YKacoqwd6XwHZM94XU1qYyZAyZ0GN2\nzCkxvYwuw9tYbKeQZVixDePVbzvmxJe+UXtJ8XI0VO9HctqwXrNjktOGO7odw/C2H4Y46S5YMFgl\n3BOT0pEzYiZyRsz0PeZydaKx9nB3O2bHm6irKgKUq9ddqOnZ4xEXn2jiTxA9hrd9hdxOEZFBAP4F\nIAnu8H9XKfWrHsewnUJRsUqw90Uphbbmyl43K7U0HkfG4Al+d6K6Z8lYvR3D4LYOQ9opSqk2EblQ\nKdUsIvEA1ovIx0qpTZG8MVFf+gsWswNeRJCcNgzJacMwfOwFvsc725tQX/2lb8pj6d73UV+9D4NS\nc3uN2lPS80xtxzC4nSesdopSqtnz6SDPc3sN42cWdP+Cbi3S7qIpkVXbMglJaRiSdxqG5J3me0y5\nutBY192OObTrLdRV7oHL1RUw5TErtwAZ2Sfp1o5haDtfWLNTRCQOwBYAJwNYopR6oMf31YrNHb2e\nxzAnM5kd8v5am/zaMZ6lBloavkJ69kndI/ah7umPiYMywnptBrZ9GX7HpohkAvgbgB8rpfb4Pa6+\nc9vDvuOmnn4Bps66IOC5DHSyKrPCvrOjGfUn9gX02utPfIlBqUP6aMeMwGlnjTelTtLOoaJ1OFy0\nzvf1uuWPG3/bvYg8DKBJKfW832N9jsSDYaCTU/X3D0IoI2aXqwvV5ftRdqQQZSU7UHZkB8pKCtHZ\n3oK8sdORlz8deWOnIS9/OnJHFSAhIUm74slwhozERSQXQIdSqk5EUgB8AuAppdRHfseEFeJeDHOi\n0DTWlXtCvRBlJYUoO1KI2srDyB15iifY3QE/PH8aUtKyzS6XQmRUiE8F8AaAOM/Hn5RST/Q4JqIQ\n98dAJwpPe1szKo7uRtmRQpSXuEfs5aU7kZKeg7z8aX4j9+nIzh3r6JuV7MpSqxhGG+L+GOhEkXG5\nXKipOOA3YneHe3tbU8CIPW/sNAwdNYXtGJM5NsS9GOZE2misq/CN1r1tmZqKg8jJmxgwYh+ePw2p\n6UPMLjdmOD7E/THQibTV0d6CiqN7fD32shJ3WyYlbYjv4qk34LOHjmM7RgcxFeL+GOhE+nC5XKip\nPNjdZ/fMkmlrqcfwfL9gHzsdw0ZNQULiILNLtrWYDXEvhjmRMZoaqvxC3T1yry4/gCF5EwJ77fnT\nkJqRY3a5thHzIe6PgU5krI72VlQe29M9p93TjhmUktk9O8bXjhmPuLg4s0u2HIZ4EAx0InO4XC7U\nVh0OGLGXlexAa1Ntr2mPQ0dNQWJSstklm4ohHgIGOpH5mhtOBIzWy44U4kTZPgwedlJAsOeNnY60\njFyzyzUMQzxMDHQi6+jsaHO3Y7y9ds/oPSk5wxPs3S2ZwUNPcmQ7hiEeBQY6kfUopVBbeThgPntZ\nyQ60NJ7A8DFTA2fHjD4ViUkpZpccFYa4BhjmRNbX0lTTa8R+4viXGDxsfK+1Y9KzhpldbsgY4hpj\noBPZR2dHGyq/KkLZkR3dd6MeKURCUkr3ao+ecB8yfIIl2zEMcR0x0InsRymFuhMlASP2siM70NxY\nhWGjvxZwEXXY6FORNCjV1HoZ4gZhoBPZW0tTba+1Y6qO70V2bn6PhcGmIz1ruGF1McRNwEAncobO\nznZUfVXcvdqjZ+SekDCo1+wYdzsmXvMaGOImY6ATOYu7HVMaMJ+9rGQHGuvKMWz0qYErPo7+GpKS\n06J6P4a4hTDQiZyrtbkO5aU7A3rtlV8VIytnTMC0x7z86cjIzgv5dRniFsVAJ3K+rs4OVB0v9oT6\nTk9bZjvi4hM9i4FN9QV7zohJAe2Y6opD+PTdBdj52dsMcatjoBPFDqUU6muO9Zod01h73NeOyRw8\nCps/fQUNNV95n8MQtwsGOlFsam2pR3nJTpSX7MBnK19ATcVB3/cY4jbGUCeKPa8vvBiHi9b5vo40\nxBM0q4giNrOg+8+OgU4UG1qb6zR5HYa4xTDQiZxv89pX0VRXiaycfNSdKInqtRjiFsZAJ3KeHRve\nxrq/PYFbHloNkXjf7JRIsSduUwx1Ivsp3rICHyy9EzffvxLDRp/qezyaeeKaj8RPzT4CANhdO1br\nlyY/HKUT2cuBXWuw4rUf4rs/WxEQ4NHSrZ3CMDcOA53I2kq+3IC/vngT/tddf8Kok07X9LV174l7\nwxxgoBvBP9ABhjqR2b46vA1/euG/cO0dSzH2lHM1f31DL2wy0I3HUTqReSqO7cGyZ+fhivm/xYRp\nl+jyHiGHuIiMBvAmgOEAXABeUUr9JtI3ZrvFeAx0IuNUVxzEH5+5Ahd/ZyEKZl2t2/uEMxLvBHCv\nUmq7iKQD2CIiq5RSxdEUwNG5Odh2IdJPffUxvPnUt3Delfdh+rnf0/W9Qg5xpVQZgDLP540iUgRg\nFICoQtwfA908HKUTaaOpvhJvPj0Xs75xG8745u26v19EPXERGQdgBoDPtSzGHwPdPBylE0WmpakW\nf3jmMkw541qce8XPDHnPsEPc00p5F8BdSqnGnt9/4YUXfJ+feeaZmDNnTlQFAuyfm42hTjSwttZG\nvPXsVRh7ynm48LoF/R57qGhdwOJX0Qjrjk0RSQDwIYCPlVIv9PF9dWD/fk0KGwgD3RoY6ERAR3sr\nlj1/NbJz8nHl919CXFxcWM838o7N/wGwp68ANxrbLdbAUTrFuq7ODvzlt/+N1PQhuPL7vws7wKMV\nzhTDcwB8F8BOEdkGQAH4pVJqpV7FhYqBbh0MdYolLlcXlv/+ViilcM0drwdsvWaUcGanrAdgfIVh\nYv/cWhjq5FRKKXy49E401pbjuz97HwkJSabU4dilaDk6tyaGOjmBUgqfLPsFykt34ab7PkZiUopp\ntTg2xP0x0K2LoU529M/lj+HQ7rW45cF/YFBKhqm1xESI+2OgWxtDnaxuw0eLsGvjnzH/wTVISRts\ndjmxF+L+GOjWx1AnK9m89lVsWv07zH9oDdKzhptdDoAYD3F/DHR7YKiTWXzbqj24Glk5Y8wux4ch\n3gfOcLEPhjoZoXjLCnyy7Be4+f6VyBk+wexyAjDE+8HRuf30DHWAwU7R0WtbNa0wxEPEQLcvjtYp\nUnpuq6YVhngEGOj2xtE6hULvbdW0whCPEgPdGRjs5M+IbdW0whDXEAPdWRjsscmobdW0whDXCQPd\nmRjszmbktmpaYYgbgIHubAx2ZzB6WzWtaB7iI0o3AQCOj5mt9Us7AgM9NjDY7cWMbdW0ottI3Bvm\nAAM9GAZ6bOkr2AGGu9nC2VbNigxppzDQB+Yf6ABDPZYw3M3T0d6KdxZfj6EjJ+PS7z4LkYh2SDOV\n4T1xtltCw1E6Mdz11dXZgXeX3GDatmpaMe3CJkfnoWOgk79g4Q4w4EPl3VbN5XKZtq2aViwxO4WB\nHjoGOvWHAT8w97ZqPzZ9WzWtWCLE/THQQ8dAp3Aw4N0Bvurt+1BeutP0bdW0YrkQ98f+eegY6BSN\n/gLeywlB/8/lj+HgrjWmb6sWyvkOlaVD3Iuj8/BwpgvpIZzgsWLgb/hoEXZ99ifMf2itIduqaRnU\n/bFFiPtjoIePo3QyWqQBplf4a7WtmlHBHA7bhbg/Bnr4GOhkZXqE5LqVb2PDh4/jqVfWYOSYfM1f\n32y2DnF/7J+Hj20XcrqN/1yB1xb9HI8tWYmRY6y1rZpWHBPiXhydR46jdHKS7Z+vwZIn7sAjL6zA\n2AlfM7sc3TguxP0x0CPHQCc727N9PZ576Ebc/8yfMXHKLLPL0ZWjQ9wfAz1ybLuQnRwo3oonf/Ff\nuOfR13HqadbdVk0rIYe4iLwG4AoA5UqpafqVpD8GenQ4SierKjm4B4/eNQ8/emAJZp5l7W3VtBLO\nSHwpgP8H4E2dajEFL4hGh6N0soqyowex4CeX45afPomzLrT+tmpaCTnElVL/ERHH/g3l6FwbHKWT\nGU5UHMPDd87F9fPvw4WX22NbNa3ETE88HAx0bXCUTkaoq6nEwz+ai7nX/gCXXX+H2eUYjiE+AAa6\ndjhKJ601NtTikTu/hbMvuhbX3WyvbdW0onmIP/76u77Pz58xBefPmKL1W5iGga4djtIpWi3NjXj0\nrivxtZnn4bt3LDC7nLDs3LwOO7es0+S1RKnQ1yoQkXEAPlBKTQ3yfdX86TJNCrMTBrr2GOrUn/a2\nVjx2zzwMzcvHjx962ba78nhdNSsRSqmI1hwI+ScXkWUANgCYJCIlIjK/r+Pav9gQSR22NqJ0k++D\ntHFq9hHfB5G/zs4OPPPADcjIysGdD75k+wCPVjizU24I9Vj/IE864+wwS7I3tly0x9YLeXV1dWHx\n/70VLlcX7nn0dcTH23dbNa3ofmGTge7GQNcOQz02KaXwu6fuRM2JMjyyeAUSE+29rZpWDJ2d4g30\nWAtzgIGuJ4a68yml8D+Lf4HD+3bi0SUrMSjZ/tuqacWUKYaxPDoHGOh6Y6g7zzuvPI7CTWuw8OU1\nSE0zb1s1KzJ9njgDnYGuN4a6vf3tj4vwr5XvYOEra5Geqf+2anZjeoj7i+V2C8BANwpD3T5WvvcK\nPvzzi3jy92sxOCfybdWczFIh7hXro3OAgW4khro1rVv5Nv706hN44uV/YGjeGLPLsSxLhrg/BjoD\n3WgMdfPFwrZqWrF8iPtjoDPQzcBQN1asbKumFVuFuL9Y758DDHSzMNT1s2f7ejz74PfwwK//4vht\n1bRi2xD34ujcrect/wx14/S1NACDPXwHirfiyZ9/G/c+9kZMbKumFduHuD8GejeO0s3F0Xp4vNuq\n/TCGtlXTiqNC3B8DvRsD3XwM9eD8t1U7+xvXmF2O7Tg2xP0x0Lsx0K2BLRi3WN5WTSsxEeL+GOjd\nGOjWEmvBHuvbqmkl5kLcH2e4dOOFUWtyahuG26ppJ6ZD3Iuj8944SrcmJ4zW7bytmhUxxHtgoPfG\nQLc2OwV7e1srFv7sOoweNxnfv/c5iES0Ixn5YYj3g4HeG9su9mDFYOe2avoIa6PkAV9MRG35xjk4\nee5pmr2mFTHQ+8ZAtx+jgr2rqwuLHrkFzU31eODXf+GuPD1Es1GyLiHuj4Eemxjo9qZluCulsGTh\nD3G89AAeWbyCu/L0wdIh7uX0MAcY6P1hqNtfJMHu3VatqHADHl2ykrvyBGGLEPfHQI9tDHRn6S/c\n3/79Y/js0+VY+PIa7srTD9uFuD8GOjHUnemJ376HT957FQtf4a48A7F1iHvFQpgDDPSBMNCd4e13\n3sFLL73TjfAgAAAGU0lEQVSEt5ctw8iRIwO+Z/YsGStyRIj7Y6CTF0PdflasWIGnn34ab731FsaN\nGxfWc2M14B0X4v4Y6OTFQLe+1atX46GHH8abb76JUyZN0vS1nRzwjg5xfwx08sdQt5b169fj7nvu\nwWuvvYZpU6ca+t52D/iYCXGvWAlzgIEeKga6ubZs3Yo7br8dL774Is444wyzy+nF6iFvWIiLyFwA\niwHEAXhNKfV0j+8bEuL+GOjUF4a6cXbt2oX5t96K5559Fueff77Z5UTMzKA3JMRFJA7AlwAuAvAV\ngC8AfEcpVex3jOEh7i/UQP/3gaM47+TROlcTvf7qtFKg/2v7Hpw/Y4rZZfTr+JjZ2LhxI+bMmWN2\nKQOyQ53eGvft24cbb7oJv1qwAJdeeqnZZfWix7nUI+yjCfFwFsCaDWCfUuoIAIjIOwDmASju91kG\nOrBym+/z/gL9PweO2SLE+6vTSotz2SHER5Ruwu7V7+GaUe5Fl6w8Uv/8888tG+KlpaV4ftEibNmy\nBZMnT0ZhYSHuv+8+SwY4oM+57GtxsYHoOcoPJ8RHASj1+/oo3MFuSaEGuhNYKdDtgsvrhq+0tBQ3\n3XwzSkpKAADHjh3D4MGDMWvWLJMrs75Igj9UMbEW5IGV2wJC3cnav9gQEOo0sBGlm3wfFNzzixb5\nAtyrpqYGzy9aZFJFBITXE58DYIFSaq7n6/sBKP+LmyKi3VQXIqIYYsSFzXgAe+G+sHkcwCYA/62U\nKorkjYmIKHoh98SVUl0i8mMAq9A9xZABTkRkIk1v9iEiImNFdWFTRB4VkUIR2SYiK0UkL8hxc0Wk\nWES+FJH7onnPCOt8RkSKRGS7iPxVRDKDHHfY7+cx/CpXGHWafT6vF5FdItIlIjP7Oc7s8xlqnWaf\nz8EiskpE9orIJyKSFeQ4w89nKOdGRH4jIvs8v7czjKirjxr6rVNELhCRWhHZ6vl4yIQaXxORchHZ\n0c8x4Z9LpVTEHwDS/T7/CYDf9XFMHID9AMYCSASwHcDkaN43gjq/CSDO8/lTAJ4MctxBAIONrC3c\nOi1yPk8BMBHAWgAz+znO7PM5YJ0WOZ9PA/iF5/P7ADxlhfMZyrkB8C0Af/d8fiaAjSb8OYdS5wUA\nVpjxe+hXw7kAZgDYEeT7EZ3LqEbiSqlGvy/TALj6OMx3k5BSqgOA9yYhwyil/qGU8ta2EUCwO30E\nJk67DLFOK5zPvUqpfXCfr/6YfT5DqdP08+l5vzc8n78B4Oogxxl9PkM5N/MAvAkASqnPAWSJiNE7\nQIT6ZxjR7A+tKKX+A6Cmn0MiOpdR/0KIyOMiUgLgBgCP9HFIXzcJjYr2faNwK4CPg3xPAVgtIl+I\nyG0G1tSXYHVa7Xz2x0rnMxgrnM9hSqlyAFBKlQEYFuQ4o89nKOem5zHH+jhGb6H+GZ7laVP8XUSs\neItxROdywNkpIrIagP+/BgL3L9ODSqkPlFIPAXjI04f6CYAFYRStmYHq9BzzIIAOpdSyIC9zjlLq\nuIgMhfsvS5HnX0+r1am7UOoMgSXOpxX0U2dfvdlgsw10P58OtgVAvlKqWUS+BeBvALRd8NwkA4a4\nUuriEF9rGYCP0DvEjwHI9/t6tOcxTQ1Up4jcAuAyAN/o5zWOe/5bKSLL4f7fNE3/kmhQpyXOZ4iv\nYfr5DIHp59NzsWu4UqrcMzmgIshr6H4+ewjl3BwDMGaAY/Q2YJ3+rV+l1Mci8qKIDFFKVRtUYygi\nOpfRzk6Z4Pfl1QD6mjf+BYAJIjJWRJIAfAfAimjeN1yeJXR/DuAqpVRbkGNSRSTd83kagEsA7DKu\nytDqhAXOZw999hmtcD57lhTkcSuczxUAbvF8fjOA93seYNL5DOXcrABwk6euOQBqva0hAw1Yp39v\nWURmwz292owAFwT/XYzsXEZ5tfVdADvgvhr8PoARnsdHAPjQ77i5cN/tuQ/A/SZcFd4H4AiArZ6P\nF3vWCWC85+fYBmCnVeu0yPm8Gu7eXQvcd+9+bNHzOWCdFjmfQwD8w1PDKgDZVjmffZ0bALcD+IHf\nMb+Fe3ZIIfqZrWRmnQDuhPsfvW0ANgA404Qal8G9jHcbgBIA87U4l7zZh4jIxmJiFUMiIqdiiBMR\n2RhDnIjIxhjiREQ2xhAnIrIxhjgRkY0xxImIbIwhTkRkY/8fjgRgw4/ImS0AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "% matplotlib inline\n", "\n", "# First create a contour plot to see where the minimum would be\n", "\n", "# Define the function we aim to minimize\n", "def f(x):\n", " return np.dot(np.dot(A,x)-b,np.dot(A,x)-b)\n", "\n", "# Create a mesh grid \n", "xx = np.linspace(-3,1,100)\n", "yy = np.linspace(0,6,100)\n", "X, Y = np.meshgrid(xx, yy)\n", "Z = np.zeros(X.shape)\n", "for i in range(Z.shape[0]):\n", " for j in range(Z.shape[1]):\n", " Z[i,j] = f(np.array([X[i,j], Y[i,j]]))\n", "\n", "# Get a nice monotone colormap\n", "cmap = plt.cm.get_cmap(\"coolwarm\")\n", "\n", "# Plot the contours and the trajectory\n", "plt.contourf(X, Y, Z, cmap = cmap)\n", "plt.plot(traj[0,:], traj[1,:], 'o-k')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution to Problem 1.7" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The gradient and the Hessian of the Rosenbrock function are\n", "\n", "\\begin{equation*}\n", " \\nabla f(\\vct{x}) = \\begin{pmatrix}\n", " -400x_1(x_2-x_1^2)-2(1-x_1)\\\\\n", " 200 (x_2-x_1^2)\n", " \\end{pmatrix},\n", " \\end{equation*}\n", " \n", " \\begin{equation*}\n", " \\nabla^2f(\\vct{x}) = \\begin{pmatrix}\n", " -400x_2+1200 x_1^2+2 & -400 x_1\\\\\n", " -400 x_1 & -400 x_1\n", " \\end{pmatrix}\n", "\\end{equation*}\n", "\n", "The point $(1,1)^{\\trans}$ is a stationary point, as the gradient at this point vanishes. Moreover, with a computer program (Python or Matlab) one verifies that the eigenvalues of the Hessian matrix are positive, from which it follows that the matrix is positive definite. By the second order optimality conditions, it follows that $(1,1)^{\\trans}$ is a local minimum. Moreover, it is the only local minimum, as there is no other point for which the gradient vanishes. The contour plot looks as follows." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZAAAAEZCAYAAAC5AHPcAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nMQnEMAzDiIpJIIZhGEZU/j9gUUR2dW4oVQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def rosenbrock(X, Y):\n", " return ((1-X)**2)+100*(Y-X**2)**2\n", "\n", "xx = np.linspace(-2,2,100)\n", "yy = np.linspace(-2,2,100)\n", "X, Y = np.meshgrid(xx,yy)\n", "Z = rosenbrock(X, Y)\n", "\n", "%matplotlib inline\n", "plt.figure()\n", "levels = [0.1,0.5,1.0,2.0,5.0,10.0,50.0,100.0,200.0,400.0,600.0]\n", "cmap = plt.cm.get_cmap(\"coolwarm\")\n", "\n", "cp = plt.contour(X,Y,Z,levels,cmap = cmap)\n", "\n", "plt.title('Level sets of Rosenbrock function')\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "plt.plot([1],[1],'ro')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python [py27]", "language": "python", "name": "Python [py27]" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.12" } }, "nbformat": 4, "nbformat_minor": 0 }