{ "cells": [ { "cell_type": "markdown", "id": "cceb0582", "metadata": {}, "source": [ "# Master M2DS-SAF: TP Optimisation\n", "\n", "## Méthodes de descente: gradient, Newton" ] }, { "cell_type": "code", "execution_count": 1, "id": "aef4e820", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from dataclasses import dataclass, field" ] }, { "cell_type": "markdown", "id": "8a76258a", "metadata": {}, "source": [ "Dans ce TP sont considérés et comparés les algorithmes de gradient et de Newton sans contrainte. Il est suggéré de regarder plus particulièrement le cas d'une fonction quadratique et de la fonction banane de Rosenbrock. L'optimisation se fera par rapport à $x=(x_1,x_2)$ dans $\\mathbb{R}^2$." ] }, { "cell_type": "markdown", "id": "5ecac9f9", "metadata": {}, "source": [ "Le code suivant définit une classe avec la fonction de Rosenbrock et les méthodes grad, hess qui renvoient le gradient et le Hessien. La fonction est définie par:\n", "$$\n", "f(x) = (x_1-1)^2+\\alpha(x_1^2-x2)^2\n", "$$\n", "Il s'agit d'une fonction non convexe." ] }, { "cell_type": "code", "execution_count": 2, "id": "be59b89f", "metadata": {}, "outputs": [], "source": [ "class Rosenbrock(object):\n", " \"\"\"\n", " Class for Rosenbrock (banana-like) function (x1-1)**2+alpha*(x1**2-x2)**2\n", "\n", " Attributes\n", " ----------\n", " alpha : float, default = 100\n", "\n", " Methods\n", " -------\n", " __call__ : computes function value at x\n", " grad(x) : computes gradient at x\n", " hess(x) : computes Hessian at x\n", " \"\"\"\n", " def __init__(self, alpha=100):\n", " self.alpha = alpha\n", "\n", " def __call__(self, x):\n", " \"\"\"\n", " Computes function's value\n", "\n", " Parameters\n", " ----------\n", " x : array_like\n", "\n", " Returns\n", " -------\n", " y : float\n", " \"\"\"\n", " y = (x[0]-1)**2 + self.alpha*(x[0]**2-x[1])**2\n", " return y\n", "\n", " def grad(self, x):\n", " \"\"\"\n", " Computes function's gradient\n", "\n", " Parameters\n", " ----------\n", " x : array_like\n", "\n", " Returns\n", " -------\n", " g : array_like\n", " \"\"\"\n", " grad = np.c_[(2*(x[0]-1) + 4*self.alpha*x[0]*(x[0]**2-x[1]),\n", " -2*self.alpha*(x[0]**2-x[1]))].T\n", " return grad\n", "\n", " def hess(self, x):\n", " \"\"\"\n", " Computes function's Hessian\n", "\n", " Parameters\n", " ----------\n", " x : array_like\n", "\n", " Returns\n", " -------\n", " H : array_like\n", " \"\"\"\n", " hessian = np.empty([2, 2])\n", " hessian[0, 0] = 2 + 4*self.alpha*(3*x[0]**2-x[1])\n", " hessian[0, 1] = -4*self.alpha*x[0]\n", " hessian[1, 0] = hessian[0, 1]\n", " hessian[1, 1] = 2*self.alpha\n", " return hessian" ] }, { "cell_type": "markdown", "id": "7dbb5927", "metadata": {}, "source": [ "Le code suivant définit une classe avec une fonction quadratique et les méthodes grad, hess qui renvoient le gradient et le Hessien." ] }, { "cell_type": "code", "execution_count": 3, "id": "950de5d2", "metadata": {}, "outputs": [], "source": [ "class Quadfunc(object):\n", " \"\"\"\n", " class for quadratic function 1/2*x.T@Q@x\n", "\n", " Attributes\n", " ----------\n", " A : array_like, default = np.eye(2)\n", "\n", " Methods\n", " -------\n", " __call__ : computes function value at x\n", " grad(x) : computes gradient at x\n", " hess(x) : computes Hessian at x\n", " \"\"\"\n", " def __init__(self, Q=np.eye(2)):\n", " self.Q = Q\n", "\n", " def __call__(self, x):\n", " y = 1/2*((self.Q@x)*x).sum(axis=0)\n", " return y\n", "\n", " def grad(self, x):\n", " grad = 1/2*(self.Q+self.Q.T)@x\n", " return grad\n", "\n", " def hess(self, x):\n", " hessian = 1/2*(self.Q+self.Q.T)\n", " return hessian" ] }, { "cell_type": "markdown", "id": "58cfecb5", "metadata": {}, "source": [ "### Tracé de la fonction à étudier" ] }, { "cell_type": "code", "execution_count": 4, "id": "3d505f85", "metadata": {}, "outputs": [], "source": [ "def plotobjective(f):\n", " \"\"\"\n", " Function to draw contour plot of objective function.\n", " \n", " Parameters\n", " ----------\n", " f : objective function (given as a class with __call__, grad\n", " and hess methods)\n", " \n", " Returns\n", " -------\n", " fig : same as fig, ax returned by plt.subplots\n", " ax : same as fig, ax returned by plt.subplots\n", " \n", " Example\n", " -------\n", " objfun = Rosenbrock(100) # choisir la fonction\n", " fig1, ax1 = plotobjective(objfun)\n", " \"\"\"\n", " N = 100\n", " x = np.linspace(-1.5, 1.5, N)\n", " y = np.linspace(-1.5, 1.5, N)\n", " X, Y = np.meshgrid(x, y)\n", " z = f(np.vstack((X.ravel(), Y.ravel())))\n", "\n", " fig, ax = plt.subplots(figsize=(6, 6), num=1, clear=True)\n", " ax.contour(X, Y, z.reshape(N, N), 20, linestyles='dashed', linewidths=0.5)\n", " return fig, ax" ] }, { "cell_type": "code", "execution_count": 5, "id": "2f782688", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "objfun = Rosenbrock()\n", "fig1, ax1 = plotobjective(objfun)" ] }, { "cell_type": "markdown", "id": "55f846fb", "metadata": {}, "source": [ "### Algorithmes de gradient et de Newton\n", "\n", "Ecrire un algorithme de descente de gradient et un algorithme de Newton. On testera différentes méthodes de choix du pas (fixe, Armijo,...). Prévoir une procédure de recherche de pas par la règle d'Armijo." ] }, { "cell_type": "markdown", "id": "823de40e", "metadata": {}, "source": [ "### Test algorithme de gradient\n", "\n", "Penser à tester un pas fixe et le pas par la méthode d'Armijo avec différentes valeurs." ] }, { "cell_type": "markdown", "id": "a1a768e5", "metadata": {}, "source": [ "### Test algorithme de Newton\n", "\n", "Penser à tester un pas fixe et le pas par la méthode d'Armijo avec différentes valeurs." ] }, { "cell_type": "code", "execution_count": null, "id": "3d2cfa76", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "jupytext": { "formats": "ipynb,md" }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.12" } }, "nbformat": 4, "nbformat_minor": 5 }