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2226622_DijonValentin_RapportLabo2_Exercice3 #31

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0386189
ajout des deux fonctions pour le rapport de laboratoire 2, exercice 3
Jan 30, 2023
7c30fd8
Modification car mauvais endroit de dépôt
Jan 30, 2023
469c051
Laboratoire 3
Feb 20, 2023
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308 changes: 308 additions & 0 deletions lab1/.ipynb_checkpoints/notebook_nlpmodels-checkpoint.ipynb
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
" # MTH8408 : Méthodes d'optimisation et contrôle optimal\n",
" ## Utiliser NLPModels pour l'optimisation sans contraintes\n",
"Tangi Migot"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this tutorial, we introduce NLPModels for numerical optimization. In particular, we will see how to create a structure providing the derivatives of an optimization problem, and then how we can use Ipopt to solve it."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this short tutorial, we will use three new packages that belongs to the organization [JuliaSmoothOptimizers](https://juliasmoothoptimizers.github.io/) developed at Polytechnique Montréal."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"using Pkg; \n",
"Pkg.activate(\"nlpmodels\") # use the closed environment defined in the nlpmodels folder"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"using ADNLPModels #Pkg.add(\"ADNLPModels\")\n",
"using NLPModels #Pkg.add(\"NLPModels\")\n",
"using NLPModelsJuMP #Pkg.add(\"NLPModelsJuMP\")\n",
"using NLPModelsIpopt #Pkg.add(\"NLPModelsIpopt\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There exists an online documentation for them:\n",
"- NLPModels: [https://juliasmoothoptimizers.github.io/NLPModels.jl/latest/tutorial/](https://juliasmoothoptimizers.github.io/NLPModels.jl/latest/tutorial/)\n",
"- NLPModelsJuMP: [https://juliasmoothoptimizers.github.io/NLPModelsJuMP.jl/dev/tutorial/](https://juliasmoothoptimizers.github.io/NLPModelsJuMP.jl/dev/tutorial/)\n",
"- NLPModelsIpopt: [https://juliasmoothoptimizers.github.io/NLPModelsIpopt.jl/stable/tutorial/#Tutorial-1](https://juliasmoothoptimizers.github.io/NLPModelsIpopt.jl/stable/tutorial/#Tutorial-1)\n",
"- ADNLPModels: [https://juliasmoothoptimizers.github.io/ADNLPModels.jl/latest/tutorial/](https://juliasmoothoptimizers.github.io/ADNLPModels.jl/latest/tutorial/)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## NLPModels\n",
"\n",
"What is NLPModels? An NLPModel is a structure allowing us to easily access the derivatives of an optimization problem. There are two principle ways to create such a structure:\n",
"i) Provide the objective function to ADNLPModel, and uses Julia's automatic differentiation;\n",
"ii) Convert a problem created in JuMP to an NLPModel.\n",
"\n",
"### 1) Using automatic differentiation\n",
"\n",
"For this purpose, NLPModels has a structure called *ADNLPModel* which is used for unconstrained optimization as follows."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"using ADNLPModels #call the package ADNLPModels\n",
"\n",
"#Initialize the objective function, and an initial guess\n",
"f(x) = (x[1] - 1)^2 + 100*(x[2] - x[1]^2)^2\n",
"x0 = [-1.2; 1.0]\n",
"\n",
"#Create an ADNLPModel\n",
"nlp = ADNLPModel(f, x0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the print, we can already see a number of important information:\n",
"- *ADNLPModel - Model with automatic differentiation* as planned Julia uses the automatic differentiation.\n",
"- There are a number information relative to the size of the problem. These information are stored in the **meta**.\n",
"- There are **Counters**, which are keeping track of the number of evaluations of the objective function, gradient, hessian ..."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"print(nlp.meta)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"nlp.meta.nvar #returns the size of x"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"print(nlp.counters)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"neval_obj(nlp) #get the number of evaluation of the objective function"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To evaluate the objective function and its derivatives, we have at hand the following functions:\n",
"- `obj`\n",
"- `grad`\n",
"- `hess`\n",
"- `hprod`\n",
"- and more..."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"x = ones(2)\n",
"obj(nlp, x)\n",
"grad(nlp, x)\n",
"v = rand(2) #vector of size 2 with random numbers between 0 and 1\n",
"hprod(nlp, x, v)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It is very important to note here that the function `hess` returns only the lower triangular of the hessian matrix, since it is always a symmetric matrix and it uses less memory this way."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"hess(nlp, x)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"using LinearAlgebra"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"hprod(nlp, x, v) - Symmetric(hess(nlp, x), :L) * v"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2) Use a JuMP model\n",
"\n",
"For this purpose, we use a package associated to `NLPModels`, which is called `NLPModelsJuMP`."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"using NLPModels, NLPModelsJuMP, JuMP\n",
"\n",
"x0 = [-1.2; 1.0]\n",
"model = Model() # No solver is required\n",
"@variable(model, x[i=1:2], start=x0[i])\n",
"@NLobjective(model, Min, (x[1] - 1)^2 + 100 * (x[2] - x[1]^2)^2)\n",
"\n",
"nlp_jump = MathOptNLPModel(model)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To access the objective function and the derivatives, we proceed the exact same way as for `ADNLPModel` before."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"x = ones(2)\n",
"obj(nlp_jump, x)\n",
"grad(nlp_jump, x)\n",
"v = rand(2)\n",
"hprod(nlp_jump, x, v)\n",
"hess(nlp_jump, x) #sparse matrix"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Solve an NLPModel with Ipopt\n",
"\n",
"The problem created with `JuMP` can be solved with `Ipopt`."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"using JuMP, Ipopt\n",
"\n",
"model = Model(Ipopt.Optimizer)\n",
"x0 = [-1.2; 1.0]\n",
"@variable(model, x[i=1:2], start=x0[i])\n",
"@NLobjective(model, Min, (x[1] - 1)^2 + 100 * (x[2] - x[1]^2)^2)\n",
"optimize!(model)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The same can be achieved very easily with `NLPModels` using the package `NLPModelsIpopt` and its function `ipopt`."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"using NLPModels, NLPModelsIpopt\n",
"\n",
"nlp = ADNLPModel(x -> (x[1] - 1)^2 + 100 * (x[2] - x[1]^2)^2, [-1.2; 1.0])\n",
"stats = ipopt(nlp)\n",
"print(stats)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.8.3",
"language": "julia",
"name": "julia-1.8"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.8.3"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
6 changes: 3 additions & 3 deletions lab1/notebook_nlpmodels.ipynb
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],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.7.1",
"display_name": "Julia 1.8.3",
"language": "julia",
"name": "julia-1.7"
"name": "julia-1.8"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.7.1"
"version": "1.8.3"
}
},
"nbformat": 4,
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