University Sétif 1 FERHAT ABBAS Faculty of Sciences
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Auteur Hadil Bourdim |
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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 convergenceRésumé : 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 convergenceRésumé : 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 Exemplaires (1)
Code-barres Cote Support Localisation Section Disponibilité MAM/0841 MAM/0841 Mémoire Bibliothèque des sciences Anglais Disponible
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