{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Preconditioned steepest descent" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## [Michel Bierlaire](https://people.epfl.ch/michel.bierlaire), EPFL." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We implement the preconditioned steepest descent algorithm to find a local minimum. This is Algorithm 11.1 in Bierlaire (2015) Optimization: principles and algorithms, EPFL Press." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def preconditionedSteepestDescent(fct, x0, D, eps, maxiter = 100):\n", " \"\"\"\n", " :param fct: function that returns the value of the function, its gradient and hessian\n", " :type fct: f, g, H = fct(x)\n", " \n", " :param x0: starting point for the algorithm. \n", " :type x0: 1D numpy.array\n", " \n", " :param D: preconditioner\n", " :type D: 2D numpy.array\n", " \n", " :param eps: precision to reach.\n", " :type eps: float.\n", " \n", " :param maxiter: maximum number of iterations. Default: 100.\n", " :type maxiter: int\n", " \n", " :return: iterates, message, where iterates is the list of iterates generated by the algorithm, and message the reason why it stopped. \n", " \"\"\"\n", "\n", " # All the iterates are stored for future display.\n", " iterates = [x0]\n", " k = 0\n", " x = x0\n", " f, g, H = fct(x)\n", " while np.linalg.norm(g) > eps and k <= maxiter:\n", " d = - D @ g\n", " alpha = - np.inner(d, g) / np.inner(d, H @ d)\n", " xplus = x + alpha * d\n", " iterates.append(xplus)\n", " x = xplus\n", " f, g, H = fct(x)\n", " k = k + 1\n", " if np.linalg.norm(g) <= eps:\n", " return iterates, f'Required precision has been reached: {np.linalg.norm(g)} <= {eps}'\n", " else:\n", " return iterates, f'Maximum number of iterations reached: {maxiter}' " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider the function $f:\\mathbb{R}^2 \\to \\mathbb{R}$ defined as \\\\[ f(x_1,x_2)= x_1^2 + 11 x_2^2 + x_1 x_2 \\\\]\n", "for which the gradient is \\\\[ \\nabla f(x_1,x_2) = \\left( \\begin{array}{c} 2x_1+x_2 \\\\ 22x_2+x_1 \\end{array} \\right) \\\\] and the hessian is \\\\[ \\nabla^2 f(x_1,x_2) = \\left(\\begin{array}{cc} 2 & 1 \\\\ 1 & 22 \\end{array}\\right).\\\\]\n", "\n", "We apply the steepest descent method with initial value $x_0=(4,1)$, and $\\varepsilon = 10^{-7}$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def fct(x):\n", " f = x[0]**2 + 11 * x[1]**2 + x[0] * x[1]\n", " g = np.array([2 * x[0] + x[1], 22 * x[1] + x[0]])\n", " H = np.array([[2, 1], [1, 22]])\n", " return f, g, H\n", "\n", "x0 = np.array([4, 1])\n", "eps = 1.0e-7" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we apply without preconditioning the function. The preconditioner is therefore the identity matrix." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Required precision has been reached: 9.617831190484184e-08 <= 1e-07\n", "Number of iterations: 41\n" ] } ], "source": [ "D = np.eye(2, 2)\n", "iterates, message = preconditionedSteepestDescent(fct, x0, D, eps)\n", "print(message)\n", "niter1 = len(iterates) - 1\n", "print(f'Number of iterations: {niter1}')" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "from mpl_toolkits import mplot3d\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# Wrapper to generate data for the plot.\n", "def fplot(x, y):\n", " npx = np.array([x, y])\n", " return fct(npx)[0]" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "\n", "xmin = -0.1\n", "xmax = 4.1\n", "ymin = -1\n", "ymax = 1.1\n", "x1 = np.linspace(xmin, xmax, 50)\n", "x2 = np.linspace(ymin, ymax, 50)\n", "\n", "X, Y = np.meshgrid(x1, x2)\n", "Z = fplot(X, Y)\n", "\n", "plt.axis([xmin, xmax, ymin, ymax], \"equal\")\n", "plt.contour(X, Y, Z, 20)\n", "\n", "xiter = [iterates[k][0] for k in range(len(iterates))]\n", "yiter = [iterates[k][1] for k in range(len(iterates))]\n", "plt.plot(xiter, yiter, color='r', marker='o')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We then apply the algorithm using the following preconditioner: \\\\[ D= \\left( \\begin{array}{cc} 1 & 0 \\\\ 0 & \\frac{1}{10} \\end{array}\\right).\\\\]" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Required precision has been reached: 8.670456111480758e-08 <= 1e-07\n", "Number of iterations: 7\n" ] } ], "source": [ "D = np.array([[1, 0], [0, 1/10]])\n", "iterates, message = preconditionedSteepestDescent(fct, x0, D, eps)\n", "print(message)\n", "print(f'Number of iterations: {len(iterates) - 1}')" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "\n", "xmin = -0.1\n", "xmax = 4.1\n", "ymin = -1\n", "ymax = 1.1\n", "x1 = np.linspace(xmin, xmax, 50)\n", "x2 = np.linspace(ymin, ymax, 50)\n", "\n", "X, Y = np.meshgrid(x1, x2)\n", "Z = fplot(X, Y)\n", "\n", "plt.axis([xmin, xmax, ymin, ymax], \"equal\")\n", "plt.contour(X, Y, Z, 20)\n", "\n", "xiter = [iterates[k][0] for k in range(len(iterates))]\n", "yiter = [iterates[k][1] for k in range(len(iterates))]\n", "plt.plot(xiter, yiter, color='r', marker='o')\n", "\n", "# Generate a zoom close to the solution\n", "ax = plt.gca()\n", "axins = ax.inset_axes([0.6, -0.6, 0.9, 0.9])\n", "axins.plot(xiter, yiter, color='r', marker='o')\n", "axins.set_xlim([-0.1, 0.1])\n", "axins.set_ylim([-0.1, 0.1])\n", "# Reove the ticks on the zoomed plot\n", "axins.xaxis.set_major_locator(plt.NullLocator())\n", "axins.yaxis.set_major_locator(plt.NullLocator())\n", "ax.indicate_inset_zoom(axins)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We observe that the number of iterations has significantly decreased. Moreover, the \"zigzag\" of the iterations has almost disappeared." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now use\n", "the matrix \\\\[ D = \\frac{1}{43} \\left( \\begin{array}{cc} 22&-1 \\\\ -1&2 \\end{array} \\right), \\\\] as preconditioner." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Required precision has been reached: 0.0 <= 1e-07\n", "Number of iterations: 1\n" ] } ], "source": [ "D = np.array([[22/43, -1/43], [-1/43, 2/43]])\n", "iterates, message = preconditionedSteepestDescent(fct, x0, D, eps)\n", "print(message)\n", "print(f'Number of iterations: {len(iterates) - 1}')" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "\n", "xmin = -0.1\n", "xmax = 4.1\n", "ymin = -1\n", "ymax = 1.1\n", "x1 = np.linspace(xmin, xmax, 50)\n", "x2 = np.linspace(ymin, ymax, 50)\n", "\n", "X, Y = np.meshgrid(x1, x2)\n", "Z = fplot(X, Y)\n", "\n", "plt.axis([xmin, xmax, ymin, ymax], \"equal\")\n", "plt.contour(X, Y, Z, 20)\n", "\n", "xiter = [iterates[k][0] for k in range(len(iterates))]\n", "yiter = [iterates[k][1] for k in range(len(iterates))]\n", "plt.plot(xiter, yiter, color='r', marker='o')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The algorithm converges in one iteration. The preconditioner happens to be inverse of the second derivatives matrix." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.2" } }, "nbformat": 4, "nbformat_minor": 2 }