feat: lagrangien augmenté
This commit is contained in:
Laureηt
parent
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commit
87f0432a3d
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@ -4,7 +4,7 @@ Résolution des problèmes de minimisation sous cs d'égalités
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# Syntaxe
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# Syntaxe
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```julia
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```julia
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Lagrangien_Augmente(algo,f,c,gradf,hessf,grad_c,
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Lagrangien_Augmente(algo,f,c,gradf,hessf,grad_c,
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hess_c,x0,options)
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hess_c,x_0,options)
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```
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```
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# Entrées
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# Entrées
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@ -18,7 +18,7 @@ Lagrangien_Augmente(algo,f,c,gradf,hessf,grad_c,
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* **hessf** : (Function) la hessienne de la ftion
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* **hessf** : (Function) la hessienne de la ftion
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* **grad_c** : (Function) le gradient de la c
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* **grad_c** : (Function) le gradient de la c
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* **hess_c** : (Function) la hessienne de la c
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* **hess_c** : (Function) la hessienne de la c
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* **x0** : (Array{Float,1}) la première composante du point de départ du Lagrangien
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* **x_0** : (Array{Float,1}) la première composante du point de départ du Lagrangien
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* **options** : (Array{Float,1})
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* **options** : (Array{Float,1})
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1. **epsilon** : utilisé dans les critères d'arrêt
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1. **epsilon** : utilisé dans les critères d'arrêt
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2. **tol** : la tolérance utilisée dans les critères d'arrêt
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2. **tol** : la tolérance utilisée dans les critères d'arrêt
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@ -42,15 +42,15 @@ f(x)=100*(x[2]-x[1]^2)^2+(1-x[1])^2
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gradf(x)=[-400*x[1]*(x[2]-x[1]^2)-2*(1-x[1]) ; 200*(x[2]-x[1]^2)]
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gradf(x)=[-400*x[1]*(x[2]-x[1]^2)-2*(1-x[1]) ; 200*(x[2]-x[1]^2)]
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hessf(x)=[-400*(x[2]-3*x[1]^2)+2 -400*x[1];-400*x[1] 200]
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hessf(x)=[-400*(x[2]-3*x[1]^2)+2 -400*x[1];-400*x[1] 200]
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algo = "gct" # ou newton|gct
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algo = "gct" # ou newton|gct
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x0 = [1; 0]
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x_0 = [1; 0]
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options = []
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options = []
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c(x) = (x[1]^2) + (x[2]^2) -1.5
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c(x) = (x[1]^2) + (x[2]^2) -1.5
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grad_c(x) = [2*x[1] ;2*x[2]]
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grad_c(x) = [2*x[1] ;2*x[2]]
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hess_c(x) = [2 0;0 2]
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hess_c(x) = [2 0;0 2]
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output = Lagrangien_Augmente(algo,f,c,gradf,hessf,grad_c,hess_c,x0,options)
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output = Lagrangien_Augmente(algo,f,c,gradf,hessf,grad_c,hess_c,x_0,options)
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```
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```
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"""
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"""
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function Lagrangien_Augmente(algo, f::Function, c::Function, gradf::Function, hessf::Function, grad_c::Function, hess_c::Function, x0, options)
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function Lagrangien_Augmente(algo, f::Function, c::Function, gradf::Function, hessf::Function, grad_c::Function, hess_c::Function, x_0, options)
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if options == []
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if options == []
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epsilon = 1e-8
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epsilon = 1e-8
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@ -68,11 +68,14 @@ function Lagrangien_Augmente(algo, f::Function, c::Function, gradf::Function, he
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tau = options[6]
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tau = options[6]
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end
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end
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n = length(x0)
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delta = 2 # TODO: changer ?
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flag = -1
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L(x, lambda, mu) = f(x) + lambda' * c(x) + mu / 2 * norm(c(x))^2
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_L(x, lambda, mu) = f(x) + lambda' * c(x) + mu / 2 * norm(c(x))^2
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gradL(x, lambda, mu) = gradf(x) + lambda' * grad_c(x) + mu / 2 * c(x) # à vérifier
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_gradL(x, lambda, mu) = gradf(x) + lambda' * grad_c(x) + mu * c(x) * grad_c(x)
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_hessL(x, lambda, mu) = hessf(x) + lambda' * hess_c(x) + mu * (c(x) * hess_c(x) + grad_c(x) * grad_c(x)')
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n = length(x_0)
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flag = -1
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eta_chap_0 = 0.1258925
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eta_chap_0 = 0.1258925
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alpha = 0.1
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alpha = 0.1
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@ -82,22 +85,26 @@ function Lagrangien_Augmente(algo, f::Function, c::Function, gradf::Function, he
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k = 0
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k = 0
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x_k = x_0
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x_k = x_0
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x_k1 = x_0
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lambda_k = lambda_0
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lambda_k = lambda_0
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mu_k = mu_0
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mu_k = mu_0
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eta_k = eta_0
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epsilon_k = epsilon_0
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while true
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while true
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L(x) = _L(x, lambda_k, mu_k)
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gradL(x) = _gradL(x, lambda_k, mu_k)
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hessL(x) = _hessL(x, lambda_k, mu_k)
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# a
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# a
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if algo == "newton"
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if algo == "newton"
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x_k1, _, _, _ = Algorithme_De_Newton(L, gradL, hessL, x_k, options)
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x_k1, _, _, _ = Algorithme_De_Newton(L, gradL, hessL, x_k, [itermax epsilon tol])
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# A FINIR
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elseif algo == "cauchy" || algo == "gct"
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elseif algo == "cauchy"
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x_k1, _, _, _ = Regions_De_Confiance(algo, L, gradL, hessL, x_k, [10 0.5 2 0.25 0.75 2 itermax epsilon tol])
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s_k = Gradient_Conjugue_Tronque(gradf(x_k), hessf(x_k), [delta_k max_iter Tol_rel])
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elseif algo == "gct"
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s_k, e_k = Pas_De_Cauchy(gradf(x_k), hessf(x_k), delta_k)
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end
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end
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if norm(c_k1) <= eta_k # b
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if norm(c(x_k1)) <= eta_k # b
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lambda_k1 = lambda_k + mu_k * c(x_k1)
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lambda_k1 = lambda_k + mu_k * c(x_k1)
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mu_k1 = mu_k
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mu_k1 = mu_k
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epsilon_k1 = epsilon_k / mu_k
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epsilon_k1 = epsilon_k / mu_k
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@ -110,7 +117,7 @@ function Lagrangien_Augmente(algo, f::Function, c::Function, gradf::Function, he
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end
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end
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if norm(gradL(x_k, lambda_k, 0)) <= max(tol * norm(gradL(x_0, lambda_0, 0)), epsilon) && norm(c(x_k)) <= max(tol * norm(c(x_0), epsilon))
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if norm(_gradL(x_k, lambda_k, 0)) <= max(tol * norm(_gradL(x_0, lambda_0, 0)), epsilon) && norm(c(x_k)) <= max(tol * norm(c(x_0), epsilon))
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flag = 0
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flag = 0
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break
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break
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elseif k >= max_iter
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elseif k >= max_iter
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@ -125,7 +132,7 @@ function Lagrangien_Augmente(algo, f::Function, c::Function, gradf::Function, he
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end
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end
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xmin = xkp1
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xmin = x_k1
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f_min = f(xmin)
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f_min = f(xmin)
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return xmin, f_min, flag, k
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return xmin, f_min, flag, k
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end
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end
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@ -14,50 +14,9 @@
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},
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},
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{
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{
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"cell_type": "code",
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"cell_type": "code",
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"execution_count": 29,
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"execution_count": null,
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"metadata": {},
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"metadata": {},
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"outputs": [
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"outputs": [],
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"\n",
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"\u001b[90m @ \u001b[39m\u001b[90m~/Documents/Cours/ENSEEIHT/S7 - Optimisation numérique/optinum/test/\u001b[39m\u001b[90m\u001b[4mtester_regions_de_confiance.jl:83\u001b[24m\u001b[39m\u001b[90m [inlined]\u001b[39m\n",
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" [5] \u001b[0m\u001b[1mmacro expansion\u001b[22m\n",
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"\u001b[90m @ \u001b[39m\u001b[90m/usr/share/julia/stdlib/v1.7/Test/src/\u001b[39m\u001b[90m\u001b[4mTest.jl:1283\u001b[24m\u001b[39m\u001b[90m [inlined]\u001b[39m\n",
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" [6] \u001b[0m\u001b[1mtester_regions_de_confiance\u001b[22m\u001b[0m\u001b[1m(\u001b[22m\u001b[90mafficher\u001b[39m::\u001b[0mBool, \u001b[90mRegions_De_Confiance\u001b[39m::\u001b[0mtypeof(Regions_De_Confiance)\u001b[0m\u001b[1m)\u001b[22m\n",
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"\u001b[90m @ \u001b[39m\u001b[35mMain\u001b[39m \u001b[90m~/Documents/Cours/ENSEEIHT/S7 - Optimisation numérique/optinum/test/\u001b[39m\u001b[90m\u001b[4mtester_regions_de_confiance.jl:39\u001b[24m\u001b[39m\n",
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"\u001b[0m\u001b[1mTest Summary: | \u001b[22m\u001b[32m\u001b[1mPass \u001b[22m\u001b[39m\u001b[91m\u001b[1mFail \u001b[22m\u001b[39m\u001b[36m\u001b[1mTotal\u001b[22m\u001b[39m\n",
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"La méthode des RC | \u001b[32m 5 \u001b[39m\u001b[91m 5 \u001b[39m\u001b[36m 10\u001b[39m\n",
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" avec Cauchy | \u001b[32m 3 \u001b[39m\u001b[91m 2 \u001b[39m\u001b[36m 5\u001b[39m\n",
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" avec GCT | \u001b[32m 2 \u001b[39m\u001b[91m 3 \u001b[39m\u001b[36m 5\u001b[39m\n",
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"\u001b[32m\u001b[1m Status\u001b[22m\u001b[39m `~/.julia/environments/v1.7/Project.toml`\n",
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" \u001b[90m [0c46a032] \u001b[39mDifferentialEquations v6.20.0\n",
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" \u001b[90m [a6016688] \u001b[39mTestOptinum v0.1.0 `https://github.com/mathn7/TestOptinum.git#master`\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
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"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.7/Project.toml`\n",
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"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.7/Manifest.toml`\n",
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"\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m project...\n",
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"\u001b[32m ✓ \u001b[39mTestOptinum\n",
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" 1 dependency successfully precompiled in 1 seconds (169 already precompiled, 2 skipped during auto due to previous errors)\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"tester_lagrangien_augmente"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"source": [
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"using Pkg\n",
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"using Pkg\n",
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"Pkg.status()\n",
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"Pkg.status()\n",
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@ -75,21 +34,9 @@
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},
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},
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{
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{
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"cell_type": "code",
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"cell_type": "code",
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"execution_count": 30,
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"execution_count": null,
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"metadata": {},
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"metadata": {},
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"outputs": [
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"outputs": [],
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{
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"data": {
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"text/plain": [
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"2-element Vector{Float64}:\n",
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" 1.0\n",
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" 0.01"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"source": [
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"# Fonction f0\n",
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"# Fonction f0\n",
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"# -----------\n",
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"# -----------\n",
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@ -143,79 +90,9 @@
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},
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},
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{
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{
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"cell_type": "code",
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"cell_type": "code",
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"execution_count": 31,
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"execution_count": null,
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"metadata": {},
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"metadata": {},
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"outputs": [
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"outputs": [],
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"-------------------------------------------------------------------------\n",
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"\u001b[34m\u001b[1mRésultats de : Newton appliqué à f0 au point initial -1.5707963267948966:\u001b[22m\u001b[39m\n",
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" * xsol = -1.5707963267948966\n",
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" * f(xsol) = -1.0\n",
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" * nb_iters = 0\n",
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" * flag = 0\n",
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" * sol_exacte : -1.5707963267948966\n",
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"-------------------------------------------------------------------------\n",
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"\u001b[34m\u001b[1mRésultats de : Newton appliqué à f0 au point initial -1.0707963267948966:\u001b[22m\u001b[39m\n",
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" * xsol = -1.5707963267949088\n",
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" * f(xsol) = -1.0\n",
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" * nb_iters = 3\n",
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" * flag = 0\n",
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" * sol_exacte : -1.5707963267948966\n",
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"-------------------------------------------------------------------------\n",
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"\u001b[34m\u001b[1mRésultats de : Newton appliqué à f0 au point initial 1.5707963267948966:\u001b[22m\u001b[39m\n",
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" * xsol = 1.5707963267948966\n",
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" * f(xsol) = 1.0\n",
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" * nb_iters = 0\n",
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" * flag = 0\n",
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" * sol_exacte : -1.5707963267948966\n",
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"-------------------------------------------------------------------------\n",
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"\u001b[34m\u001b[1mRésultats de : Newton appliqué à f1 au point initial [1, 1, 1]:\u001b[22m\u001b[39m\n",
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" * xsol = [1, 1, 1]\n",
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" * f(xsol) = 0\n",
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" * nb_iters = 0\n",
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" * flag = 0\n",
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" * sol_exacte : [1, 1, 1]\n",
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"-------------------------------------------------------------------------\n",
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"\u001b[34m\u001b[1mRésultats de : Newton appliqué à f1 au point initial [1, 0, 0]:\u001b[22m\u001b[39m\n",
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" * xsol = [1.0000000000000002, 1.0, 0.9999999999999998]\n",
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" * f(xsol) = 9.860761315262648e-32\n",
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" * nb_iters = 1\n",
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" * flag = 0\n",
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" * sol_exacte : [1, 1, 1]\n",
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"-------------------------------------------------------------------------\n",
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"\u001b[34m\u001b[1mRésultats de : Newton appliqué à f1 au point initial [10.0, 3.0, -2.2]:\u001b[22m\u001b[39m\n",
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" * xsol = [1.0, 0.9999999999999996, 0.9999999999999982]\n",
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" * f(xsol) = 1.1832913578315177e-29\n",
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" * nb_iters = 1\n",
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" * flag = 0\n",
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" * sol_exacte : [1, 1, 1]\n",
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"-------------------------------------------------------------------------\n",
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"\u001b[34m\u001b[1mRésultats de : Newton appliqué à f2 au point initial [1.0, 0.01]:\u001b[22m\u001b[39m\n",
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" * xsol = [1.0, 1.0]\n",
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" * f(xsol) = 9801.0\n",
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" * nb_iters = 1\n",
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" * flag = 0\n",
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" * sol_exacte : [1.0, 0.01]\n",
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"-------------------------------------------------------------------------\n",
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"\u001b[34m\u001b[1mRésultats de : Newton appliqué à f2 au point initial [-1.2, 1.0]:\u001b[22m\u001b[39m\n",
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" * xsol = [1.0000000000000238, 0.9999999999815201]\n",
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" * f(xsol) = 9800.999999634088\n",
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" * nb_iters = 6\n",
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" * flag = 0\n",
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" * sol_exacte : [1.0, 0.01]\n",
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"-------------------------------------------------------------------------\n",
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"\u001b[34m\u001b[1mRésultats de : Newton appliqué à f2 au point initial [10, 0]:\u001b[22m\u001b[39m\n",
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" * xsol = [1.000000000000007, 1.0000000000000142]\n",
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" * f(xsol) = 9801.000000000278\n",
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" * nb_iters = 5\n",
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" * flag = 0\n",
|
|
||||||
" * sol_exacte : [1.0, 0.01]\n"
|
|
||||||
]
|
|
||||||
}
|
|
||||||
],
|
|
||||||
"source": [
|
"source": [
|
||||||
"# Affichage les sorties de l'algorithme de Newton\n",
|
"# Affichage les sorties de l'algorithme de Newton\n",
|
||||||
"function my_afficher_resultats(algo, nom_fct, point_init, xmin, fxmin, flag, sol_exacte, nbiters)\n",
|
"function my_afficher_resultats(algo, nom_fct, point_init, xmin, fxmin, flag, sol_exacte, nbiters)\n",
|
||||||
|
|
@ -266,27 +143,9 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 32,
|
"execution_count": null,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [],
|
||||||
{
|
|
||||||
"name": "stdout",
|
|
||||||
"output_type": "stream",
|
|
||||||
"text": [
|
|
||||||
"\u001b[0m\u001b[1mTest Summary: | \u001b[22m\u001b[32m\u001b[1mPass \u001b[22m\u001b[39m\u001b[36m\u001b[1mTotal\u001b[22m\u001b[39m\n",
|
|
||||||
"L'algo de Newton | \u001b[32m 14 \u001b[39m\u001b[36m 14\u001b[39m\n"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"data": {
|
|
||||||
"text/plain": [
|
|
||||||
"Test.DefaultTestSet(\"L'algo de Newton\", Any[Test.DefaultTestSet(\"Cas test 1 x0 = solution\", Any[Test.DefaultTestSet(\"solution\", Any[], 1, false, false), Test.DefaultTestSet(\"itération\", Any[], 1, false, false)], 0, false, false), Test.DefaultTestSet(\"Cas test 1 x0 = x011\", Any[Test.DefaultTestSet(\"solution\", Any[], 1, false, false), Test.DefaultTestSet(\"itération\", Any[], 1, false, false)], 0, false, false), Test.DefaultTestSet(\"Cas test 1 x0 = x012\", Any[Test.DefaultTestSet(\"solution\", Any[], 1, false, false), Test.DefaultTestSet(\"itération\", Any[], 1, false, false)], 0, false, false), Test.DefaultTestSet(\"Cas test 2 x0 = solution\", Any[Test.DefaultTestSet(\"solution\", Any[], 1, false, false), Test.DefaultTestSet(\"itération\", Any[], 1, false, false)], 0, false, false), Test.DefaultTestSet(\"Cas test 2 x0 = x021\", Any[Test.DefaultTestSet(\"solution\", Any[], 1, false, false), Test.DefaultTestSet(\"itération\", Any[], 1, false, false)], 0, false, false), Test.DefaultTestSet(\"Cas test 2 x0 = x022\", Any[Test.DefaultTestSet(\"solution\", Any[], 1, false, false), Test.DefaultTestSet(\"itération\", Any[], 1, false, false)], 0, false, false), Test.DefaultTestSet(\"Cas test 2 x0 = x023\", Any[Test.DefaultTestSet(\"solution\", Any[], 1, false, false), Test.DefaultTestSet(\"exception\", Any[], 1, false, false)], 0, false, false)], 0, false, false)"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
"metadata": {},
|
|
||||||
"output_type": "display_data"
|
|
||||||
}
|
|
||||||
],
|
|
||||||
"source": [
|
"source": [
|
||||||
"tester_algo_newton(false, Algorithme_De_Newton)"
|
"tester_algo_newton(false, Algorithme_De_Newton)"
|
||||||
]
|
]
|
||||||
|
|
@ -342,28 +201,9 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 33,
|
"execution_count": null,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [],
|
||||||
{
|
|
||||||
"name": "stdout",
|
|
||||||
"output_type": "stream",
|
|
||||||
"text": [
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : Cauchy 1\u001b[22m\u001b[39m\n",
|
|
||||||
" * s = [0, 0]\n",
|
|
||||||
" * e = 0\n",
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : Cauchy 2\u001b[22m\u001b[39m\n",
|
|
||||||
" * s = [-0.9230769230769234, -0.30769230769230776]\n",
|
|
||||||
" * e = 1\n",
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : Cauchy 3\u001b[22m\u001b[39m\n",
|
|
||||||
" * s = [0.8944271909999159, -0.4472135954999579]\n",
|
|
||||||
" * e = -1\n"
|
|
||||||
]
|
|
||||||
}
|
|
||||||
],
|
|
||||||
"source": [
|
"source": [
|
||||||
"function my_afficher_resultats_cauchy(algo, s, e)\n",
|
"function my_afficher_resultats_cauchy(algo, s, e)\n",
|
||||||
" println(\"-------------------------------------------------------------------------\")\n",
|
" println(\"-------------------------------------------------------------------------\")\n",
|
||||||
|
|
@ -393,68 +233,18 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 34,
|
"execution_count": null,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [],
|
||||||
{
|
|
||||||
"name": "stdout",
|
|
||||||
"output_type": "stream",
|
|
||||||
"text": [
|
|
||||||
"Cauchy 4 = [5.000000000000001, -2.5000000000000004]\n",
|
|
||||||
"Cauchy 5= [4.47213595499958, -2.23606797749979]\n",
|
|
||||||
"Cauchy 6= [-4.743416490252569, -1.5811388300841895]\n",
|
|
||||||
"Cauchy 6= [-2.23606797749979, -4.47213595499958]\n",
|
|
||||||
"\u001b[0m\u001b[1mTest Summary: | \u001b[22m\u001b[32m\u001b[1mPass \u001b[22m\u001b[39m\u001b[36m\u001b[1mTotal\u001b[22m\u001b[39m\n",
|
|
||||||
"Pas de Cauchy | \u001b[32m 7 \u001b[39m\u001b[36m 7\u001b[39m\n"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"data": {
|
|
||||||
"text/plain": [
|
|
||||||
"Test.DefaultTestSet(\"Pas de Cauchy\", Any[Test.DefaultTestSet(\"g = 0\", Any[], 1, false, false), Test.DefaultTestSet(\"quad 2, non saturé\", Any[], 1, false, false), Test.DefaultTestSet(\"quad 2, saturé\", Any[], 1, false, false), Test.DefaultTestSet(\"quad 3, non saturé\", Any[], 1, false, false), Test.DefaultTestSet(\"quad 3, saturé\", Any[], 1, false, false), Test.DefaultTestSet(\"quad 3, g'*H*g <0 saturé\", Any[], 1, false, false), Test.DefaultTestSet(\"quad 3, g'*H*g = 0 saturé\", Any[], 1, false, false)], 0, false, false)"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
"metadata": {},
|
|
||||||
"output_type": "display_data"
|
|
||||||
}
|
|
||||||
],
|
|
||||||
"source": [
|
"source": [
|
||||||
"tester_pas_de_cauchy(false, Pas_De_Cauchy)"
|
"tester_pas_de_cauchy(false, Pas_De_Cauchy)"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 35,
|
"execution_count": null,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [],
|
||||||
{
|
|
||||||
"name": "stdout",
|
|
||||||
"output_type": "stream",
|
|
||||||
"text": [
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : RC-Cauchy appliqué à f0 au point initial -1.5707963267948966:\u001b[22m\u001b[39m\n",
|
|
||||||
" * xsol = -1.5707963267948966\n",
|
|
||||||
" * f(xsol) = -1.0\n",
|
|
||||||
" * nb_iters = 0\n",
|
|
||||||
" * flag = 0\n",
|
|
||||||
" * sol_exacte : -1.5707963267948966\n",
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : RC-Cauchy appliqué à f1 au point initial [1, 1, 1]:\u001b[22m\u001b[39m\n",
|
|
||||||
" * xsol = [1, 1, 1]\n",
|
|
||||||
" * f(xsol) = 0\n",
|
|
||||||
" * nb_iters = 0\n",
|
|
||||||
" * flag = 0\n",
|
|
||||||
" * sol_exacte : [1, 1, 1]\n",
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : RC-Cauchy appliqué à f2 au point initial [1.0, 0.01]:\u001b[22m\u001b[39m\n",
|
|
||||||
" * xsol = [1.0, 0.01]\n",
|
|
||||||
" * f(xsol) = 0.0\n",
|
|
||||||
" * nb_iters = 10000\n",
|
|
||||||
" * flag = 3\n",
|
|
||||||
" * sol_exacte : [1.0, 0.01]\n"
|
|
||||||
]
|
|
||||||
}
|
|
||||||
],
|
|
||||||
"source": [
|
"source": [
|
||||||
"options = [10, 0.5, 2.00, 0.25, 0.75, 2, 10000, sqrt(eps()), 1e-15]\n",
|
"options = [10, 0.5, 2.00, 0.25, 0.75, 2, 10000, sqrt(eps()), 1e-15]\n",
|
||||||
"algo = \"cauchy\"\n",
|
"algo = \"cauchy\"\n",
|
||||||
|
|
@ -511,31 +301,9 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 36,
|
"execution_count": null,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [],
|
||||||
{
|
|
||||||
"name": "stdout",
|
|
||||||
"output_type": "stream",
|
|
||||||
"text": [
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : Cauchy 1\u001b[22m\u001b[39m\n",
|
|
||||||
" * s = [2.220446049250313e-16, 1.0]\n",
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : Cauchy 2\u001b[22m\u001b[39m\n",
|
|
||||||
" * s = [0.0, 0.0]\n",
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : Cauchy 3\u001b[22m\u001b[39m\n",
|
|
||||||
" * s = [-0.4743416490252569, -0.15811388300841897]\n",
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : Cauchy 4\u001b[22m\u001b[39m\n",
|
|
||||||
" * s = [-0.8740776099190263, -0.8221850958502243]\n",
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : Cauchy 5\u001b[22m\u001b[39m\n",
|
|
||||||
" * s = [-0.8571428571428571, -0.9999999999999998]\n"
|
|
||||||
]
|
|
||||||
}
|
|
||||||
],
|
|
||||||
"source": [
|
"source": [
|
||||||
"function my_afficher_resultats_gct(algo, s)\n",
|
"function my_afficher_resultats_gct(algo, s)\n",
|
||||||
" println(\"-------------------------------------------------------------------------\")\n",
|
" println(\"-------------------------------------------------------------------------\")\n",
|
||||||
|
|
@ -576,64 +344,18 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 37,
|
"execution_count": null,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [],
|
||||||
{
|
|
||||||
"name": "stdout",
|
|
||||||
"output_type": "stream",
|
|
||||||
"text": [
|
|
||||||
"\u001b[0m\u001b[1mTest Summary: | \u001b[22m\u001b[32m\u001b[1mPass \u001b[22m\u001b[39m\u001b[36m\u001b[1mTotal\u001b[22m\u001b[39m\n",
|
|
||||||
"Gradient-CT | \u001b[32m 9 \u001b[39m\u001b[36m 9\u001b[39m\n"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"data": {
|
|
||||||
"text/plain": [
|
|
||||||
"Test.DefaultTestSet(\"Gradient-CT\", Any[], 9, false, false)"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
"metadata": {},
|
|
||||||
"output_type": "display_data"
|
|
||||||
}
|
|
||||||
],
|
|
||||||
"source": [
|
"source": [
|
||||||
"tester_gct(false, Gradient_Conjugue_Tronque)"
|
"tester_gct(false, Gradient_Conjugue_Tronque)"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 38,
|
"execution_count": null,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [],
|
||||||
{
|
|
||||||
"name": "stdout",
|
|
||||||
"output_type": "stream",
|
|
||||||
"text": [
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : RC-GCT appliqué à f0 au point initial -1.5707963267948966:\u001b[22m\u001b[39m\n",
|
|
||||||
" * xsol = -1.5707963267948966\n",
|
|
||||||
" * f(xsol) = -1.0\n",
|
|
||||||
" * nb_iters = 0\n",
|
|
||||||
" * flag = 0\n",
|
|
||||||
" * sol_exacte : -1.5707963267948966\n",
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : RC-GCT appliqué à f1 au point initial [1, 1, 1]:\u001b[22m\u001b[39m\n",
|
|
||||||
" * xsol = [1, 1, 1]\n",
|
|
||||||
" * f(xsol) = 0\n",
|
|
||||||
" * nb_iters = 0\n",
|
|
||||||
" * flag = 0\n",
|
|
||||||
" * sol_exacte : [1, 1, 1]\n",
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : RC-GCT appliqué à f2 au point initial [1.0, 0.01]:\u001b[22m\u001b[39m\n",
|
|
||||||
" * xsol = [1.0, 0.01]\n",
|
|
||||||
" * f(xsol) = 0.0\n",
|
|
||||||
" * nb_iters = 10000\n",
|
|
||||||
" * flag = 3\n",
|
|
||||||
" * sol_exacte : [1.0, 0.01]\n"
|
|
||||||
]
|
|
||||||
}
|
|
||||||
],
|
|
||||||
"source": [
|
"source": [
|
||||||
"options = [10, 0.5, 2.00, 0.25, 0.75, 2, 10000, sqrt(eps()), 1e-15]\n",
|
"options = [10, 0.5, 2.00, 0.25, 0.75, 2, 10000, sqrt(eps()), 1e-15]\n",
|
||||||
"algo = \"gct\"\n",
|
"algo = \"gct\"\n",
|
||||||
|
|
@ -653,100 +375,11 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 39,
|
"execution_count": null,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [],
|
||||||
{
|
|
||||||
"name": "stdout",
|
|
||||||
"output_type": "stream",
|
|
||||||
"text": [
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : régions de confiance avec cauchy appliqué à fonction 1 au point initial x011 :\u001b[22m\u001b[39m\n",
|
|
||||||
" * xsol = [1.0000000310867154, 0.9999999957837182, 0.999999960480721]\n",
|
|
||||||
" * f(xsol) = 2.812589785349316e-15\n",
|
|
||||||
" * nb_iters = 48\n",
|
|
||||||
" * flag = 0\n",
|
|
||||||
" * sol_exacte : [1, 1, 1]\n",
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : régions de confiance avec cauchy appliqué à fonction 1 au point initial x012 :\u001b[22m\u001b[39m\n",
|
|
||||||
" * xsol = [1.0000001114825787, 0.9999999912691591, 0.9999998710557396]\n",
|
|
||||||
" * f(xsol) = 3.027462898391515e-14\n",
|
|
||||||
" * nb_iters = 42\n",
|
|
||||||
" * flag = 0\n",
|
|
||||||
" * sol_exacte : [1, 1, 1]\n",
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : régions de confiance avec cauchy appliqué à fonction 2 au point initial x021 :\u001b[22m\u001b[39m\n",
|
|
||||||
" * xsol = [0.9993529197795769, 0.9987042941099483]\n",
|
|
||||||
" * f(xsol) = 4.1909860490578263e-7\n",
|
|
||||||
" * nb_iters = 5000\n",
|
|
||||||
" * flag = 3\n",
|
|
||||||
" * sol_exacte : [1, 1]\n",
|
|
||||||
"iters = 864\n",
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : régions de confiance avec cauchy appliqué à fonction 2 au point initial x022 :\u001b[22m\u001b[39m\n",
|
|
||||||
" * xsol = [0.9961677295964368, 0.9923393628804894]\n",
|
|
||||||
" * f(xsol) = 1.4697922911344958e-5\n",
|
|
||||||
" * nb_iters = 864\n",
|
|
||||||
" * flag = 0\n",
|
|
||||||
" * sol_exacte : [1, 1]\n",
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : régions de confiance avec cauchy appliqué à fonction 2 au point initial x023 :\u001b[22m\u001b[39m\n",
|
|
||||||
" * xsol = [0.9999372227331438, 0.9998738531186088]\n",
|
|
||||||
" * f(xsol) = 3.9765412510183685e-9\n",
|
|
||||||
" * nb_iters = 5000\n",
|
|
||||||
" * flag = 3\n",
|
|
||||||
" * sol_exacte : [1, 1]\n",
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : régions de confiance avec gct appliqué à fonction 1 au point initial x011 :\u001b[22m\u001b[39m\n",
|
|
||||||
" * xsol = [1.0000000000000007, 1.0, 1.0]\n",
|
|
||||||
" * f(xsol) = 2.0214560696288428e-30\n",
|
|
||||||
" * nb_iters = 1\n",
|
|
||||||
" * flag = 0\n",
|
|
||||||
" * sol_exacte : [1, 1, 1]\n",
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : régions de confiance avec gct appliqué à fonction 1 au point initial x012 :\u001b[22m\u001b[39m\n",
|
|
||||||
" * xsol = [0.9999999999999996, 1.0000000000000002, 1.0000000000000004]\n",
|
|
||||||
" * f(xsol) = 4.930380657631324e-31\n",
|
|
||||||
" * nb_iters = 3\n",
|
|
||||||
" * flag = 0\n",
|
|
||||||
" * sol_exacte : [1, 1, 1]\n",
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : régions de confiance avec gct appliqué à fonction 2 au point initial x021 :\u001b[22m\u001b[39m\n",
|
|
||||||
" * xsol = [0.9999996743780089, 0.9999993478371609]\n",
|
|
||||||
" * f(xsol) = 1.0611413038132374e-13\n",
|
|
||||||
" * nb_iters = 31\n",
|
|
||||||
" * flag = 0\n",
|
|
||||||
" * sol_exacte : [1, 1]\n",
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : régions de confiance avec gct appliqué à fonction 2 au point initial x022 :\u001b[22m\u001b[39m\n",
|
|
||||||
" * xsol = [1.0000035183009863, 1.0000066949336202]\n",
|
|
||||||
" * f(xsol) = 2.4053014026923312e-11\n",
|
|
||||||
" * nb_iters = 44\n",
|
|
||||||
" * flag = 0\n",
|
|
||||||
" * sol_exacte : [1, 1]\n",
|
|
||||||
"-------------------------------------------------------------------------\n",
|
|
||||||
"\u001b[34m\u001b[1mRésultats de : régions de confiance avec gct appliqué à fonction 2 au point initial x023 :\u001b[22m\u001b[39m\n",
|
|
||||||
" * xsol = [1.0000000000000007, 1.0, 1.0]\n",
|
|
||||||
" * f(xsol) = 3.1813581453548166e-24\n",
|
|
||||||
" * nb_iters = 19\n",
|
|
||||||
" * flag = 0\n",
|
|
||||||
" * sol_exacte : [1, 1]\n",
|
|
||||||
"\u001b[0m\u001b[1mTest Summary: | \u001b[22m\u001b[32m\u001b[1mPass \u001b[22m\u001b[39m\u001b[36m\u001b[1mTotal\u001b[22m\u001b[39m\n",
|
|
||||||
"La méthode des RC | \u001b[32m 10 \u001b[39m\u001b[36m 10\u001b[39m\n"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"data": {
|
|
||||||
"text/plain": [
|
|
||||||
"Test.DefaultTestSet(\"La méthode des RC \", Any[Test.DefaultTestSet(\"avec Cauchy \", Any[], 5, false, false), Test.DefaultTestSet(\"avec GCT \", Any[], 5, false, false)], 0, false, false)"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
"metadata": {},
|
|
||||||
"output_type": "display_data"
|
|
||||||
}
|
|
||||||
],
|
|
||||||
"source": [
|
"source": [
|
||||||
"tester_regions_de_confiance(true, Regions_De_Confiance)"
|
"tester_regions_de_confiance(false, Regions_De_Confiance)"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
|
|
@ -772,7 +405,10 @@
|
||||||
"cell_type": "markdown",
|
"cell_type": "markdown",
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"source": [
|
"source": [
|
||||||
"## Vos réponses?\n"
|
"1. dqzd\n",
|
||||||
|
"2. dzqd\n",
|
||||||
|
"3. 3dqzdzd\n",
|
||||||
|
"4. dqzd"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
|
|
@ -794,11 +430,63 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 40,
|
"execution_count": null,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [],
|
"outputs": [],
|
||||||
"source": [
|
"source": [
|
||||||
"# Vos tests"
|
"function afficher_resultats(algo,nom_fct,point_init,xmin,fxmin,flag,sol_exacte,nbiters)\n",
|
||||||
|
"\tprintln(\"-------------------------------------------------------------------------\")\n",
|
||||||
|
"\tprintstyled(\"Résultats de : \"*algo*\" appliqué à \"*nom_fct*\" au point initial \"*point_init*\" :\\n\",bold=true,color=:blue)\n",
|
||||||
|
"\tprintln(\" * xsol = \",xmin)\n",
|
||||||
|
"\tprintln(\" * f(xsol) = \",fxmin)\n",
|
||||||
|
"\tprintln(\" * nb_iters = \",nbiters)\n",
|
||||||
|
"\tprintln(\" * flag = \",flag)\n",
|
||||||
|
"\tprintln(\" * sol_exacte : \", sol_exacte)\n",
|
||||||
|
"end\n",
|
||||||
|
"\n",
|
||||||
|
"fct1(x) = 2 * (x[1] + x[2] + x[3] - 3)^2 + (x[1] - x[2])^2 + (x[2] - x[3])^2\n",
|
||||||
|
"# la gradient de la fonction fct1\n",
|
||||||
|
"function grad_fct1(x)\n",
|
||||||
|
" y1 = 4 * (x[1] + x[2] + x[3] - 3) + 2 * (x[1] - x[2])\n",
|
||||||
|
" y2 = 4 * (x[1] + x[2] + x[3] - 3) - 2 * (x[1] - x[2]) + 2 * (x[2] - x[3])\n",
|
||||||
|
" y3 = 4 * (x[1] + x[2] + x[3] - 3) - 2 * (x[2] - x[3])\n",
|
||||||
|
" return [y1; y2; y3]\n",
|
||||||
|
"end\n",
|
||||||
|
"# la hessienne de la fonction fct1\n",
|
||||||
|
"hess_fct1(x) = [6 2 4; 2 8 2; 4 2 6]\n",
|
||||||
|
"\n",
|
||||||
|
"contrainte1(x) = x[1] + x[3] - 1\n",
|
||||||
|
"grad_contrainte1(x) = [1; 0; 1]\n",
|
||||||
|
"hess_contrainte1(x) = [0 0 0; 0 0 0; 0 0 0]\n",
|
||||||
|
"\n",
|
||||||
|
"x01 = [0; 1; 1]\n",
|
||||||
|
"x02 = [0.5; 1.25; 1]\n",
|
||||||
|
"x03 = [1; 0]\n",
|
||||||
|
"x04 = [sqrt(3) / 2; sqrt(3) / 2]\n",
|
||||||
|
"pts2 = Pts_avec_contraintes(x01, x02, x03, x04)\n",
|
||||||
|
"\n",
|
||||||
|
"# sol_fct1_augm = [0.5 ; 1.25 ; 0.5]\n",
|
||||||
|
"\n",
|
||||||
|
"algo = \"newton\"\n",
|
||||||
|
"xmin, fxmin, flag, nbiters = Lagrangien_Augmente(algo, fct1, contrainte1, grad_fct1, hess_fct1, grad_contrainte1, hess_contrainte1, pts2.x01, options)\n",
|
||||||
|
"afficher_resultats(\"Lagrangien augmenté avec \" * algo, \"fonction 1\", \"x01\", xmin, fxmin, flag, sol_fct1_augm, nbiters)\n",
|
||||||
|
"\n",
|
||||||
|
"algo = \"cauchy\"\n",
|
||||||
|
"xmin, fxmin, flag, nbiters = Lagrangien_Augmente(algo, fct1, contrainte1, grad_fct1, hess_fct1, grad_contrainte1, hess_contrainte1, pts2.x01, options)\n",
|
||||||
|
"afficher_resultats(\"Lagrangien augmenté avec \" * algo, \"fonction 1\", \"x01\", xmin, fxmin, flag, sol_fct1_augm, nbiters)\n",
|
||||||
|
"\n",
|
||||||
|
"algo = \"gct\"\n",
|
||||||
|
"xmin, fxmin, flag, nbiters = Lagrangien_Augmente(algo, fct1, contrainte1, grad_fct1, hess_fct1, grad_contrainte1, hess_contrainte1, pts2.x01, options)\n",
|
||||||
|
"afficher_resultats(\"Lagrangien augmenté avec \" * algo, \"fonction 1\", \"x01\", xmin, fxmin, flag, sol_fct1_augm, nbiters)"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": null,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
|
"tester_lagrangien_augmente(false, Lagrangien_Augmente)"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
|
|
|
||||||
Loading…
Reference in a new issue