Titre :	On Recent Descent Methods For Large-scale Optimization
Type de document :	document électronique
Auteurs :	Hadil Bourdim, Auteur ; Lina Manel Bouzeghar, Acteur ; Ziadi, Raouf, Directeur de thèse
Editeur :	Sétif:UFS
Année de publication :	2025
Importance :	1 vol (59 f.)
Format :	29 cm
Langues :	Anglais (eng)
Mots-clés :	Unconstrained optimization Nonlinear optimization Conjugate gradient methods Line search Global convergence
Résumé :	In this study, we present a synthesis of various conjugate gradient methods for solving unconstrained optimization problems, where the objective function is nonlinear but continuously differentiable (and possibly non-convex). To illustrate the performance of these methods, numerical experiments are conducted on a set of standard test functions, along with comparative analysis.
Note de contenu :	Contents Introduction 6 1 Fundamentalnotions 7 1.1 Convexity . ................................... 7 1.2 Unconstrainedoptimizationproblem . ................... 9 1.2.1 Existenceanduniquenessresults . .................. 10 1.2.2 Descentdirection . ........................... 11 1.2.3 Generalschemeofunconstrainedoptimizationalgorithms . ... 12 1.2.4 Sufficientoptimalityconditions . ................... 14 1.2.5 Necessaryandsufficientconditions(convexcase) . ........ 14 2 Linesearchtechniques 16 2.1 Linesearch . ................................... 16 2.1.1 Exactlinesearch . ........................... 17 2.2 Uncertaintyinterval . .............................. 17 2.2.1 Inexactlinesearch . .......................... 18 2.2.2 Armijomethod . ............................ 19 2.2.3 Goldstein-Pricerule . ......................... 20 2.2.4 Wolfelinesearch . ........................... 21 2.2.5 Strongwolfelinesearch . ....................... 21 3 ConjugateGradientMethods 24 3.1 Linearconjugategradientmethods . ..................... 24 3.1.1 Conjugatedirectionsmethod . .................... 26 3.1.2 Conjugategradientmethod . ..................... 28 3.2 Nonlinearconjugategradientmethod . ................... 30 3.2.1 Zoutendijkconditionsforglobalconvergence . .......... 31 4 MZ:anewconjugategradientmethodbyadaptinganewstep-size 35 4.1 Theproposedconjugategradientalgorithm . ................ 37 4.1.1 Theconjugategradientformulaandthecorrespondingalgorithm 37 4.1.2 Thesufficientdescentproperty . ................... 37 4.2 Theglobalconvergence . ........................... 40 5 Numericalexperiments 45 5.1 DescriptionoftheTestFunctions . ...................... 45 5.2 Commentsonnumericaltests: . ........................ 52
Côte titre :	MAM/0841

On Recent Descent Methods For Large-scale Optimization [document électronique] / Hadil Bourdim, Auteur ; Lina Manel Bouzeghar, Acteur ; Ziadi, Raouf, Directeur de thèse . - [S.l.] : Sétif:UFS, 2025 . - 1 vol (59 f.) ; 29 cm.
Langues : Anglais (eng)

Mots-clés :	Unconstrained optimization Nonlinear optimization Conjugate gradient methods Line search Global convergence
Résumé :	In this study, we present a synthesis of various conjugate gradient methods for solving unconstrained optimization problems, where the objective function is nonlinear but continuously differentiable (and possibly non-convex). To illustrate the performance of these methods, numerical experiments are conducted on a set of standard test functions, along with comparative analysis.
Note de contenu :	Contents Introduction 6 1 Fundamentalnotions 7 1.1 Convexity . ................................... 7 1.2 Unconstrainedoptimizationproblem . ................... 9 1.2.1 Existenceanduniquenessresults . .................. 10 1.2.2 Descentdirection . ........................... 11 1.2.3 Generalschemeofunconstrainedoptimizationalgorithms . ... 12 1.2.4 Sufficientoptimalityconditions . ................... 14 1.2.5 Necessaryandsufficientconditions(convexcase) . ........ 14 2 Linesearchtechniques 16 2.1 Linesearch . ................................... 16 2.1.1 Exactlinesearch . ........................... 17 2.2 Uncertaintyinterval . .............................. 17 2.2.1 Inexactlinesearch . .......................... 18 2.2.2 Armijomethod . ............................ 19 2.2.3 Goldstein-Pricerule . ......................... 20 2.2.4 Wolfelinesearch . ........................... 21 2.2.5 Strongwolfelinesearch . ....................... 21 3 ConjugateGradientMethods 24 3.1 Linearconjugategradientmethods . ..................... 24 3.1.1 Conjugatedirectionsmethod . .................... 26 3.1.2 Conjugategradientmethod . ..................... 28 3.2 Nonlinearconjugategradientmethod . ................... 30 3.2.1 Zoutendijkconditionsforglobalconvergence . .......... 31 4 MZ:anewconjugategradientmethodbyadaptinganewstep-size 35 4.1 Theproposedconjugategradientalgorithm . ................ 37 4.1.1 Theconjugategradientformulaandthecorrespondingalgorithm 37 4.1.2 Thesufficientdescentproperty . ................... 37 4.2 Theglobalconvergence . ........................... 40 5 Numericalexperiments 45 5.1 DescriptionoftheTestFunctions . ...................... 45 5.2 Commentsonnumericaltests: . ........................ 52
Côte titre :	MAM/0841