New Variant Of The Conjugate Gradient Method With Practical Application / Malika Kerour

Public ISBD Titre : New Variant Of The Conjugate Gradient Method With Practical Application Type de document : texte imprimé Auteurs : Malika Kerour, Auteur ; Hanaa Hemissi, Auteur ; Khelladi ,Samia, Directeur de thèse Editeur : Sétif:UFA1 Année de publication : 2025 Importance : 1 vol (49 f.) Format : 29 cm Langues : Anglais (eng) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Nonlinear unconstrained optimization Conjugate gradient method Descent direction Global convergence Inexact line search Index. décimale : 510-Mathématique Résumé : Abstract The conjugate gradient method is one of the most effective methods for solving unconstrained nonlinear optimization problems, as well as for solving large dimensional linear systems. In this dissertation, we propose a new conjugate gradient method, characterized by an improved descent direction and a new WYL-type parameter, denoted YHS, followed by a comprehensive theoretical study. We carried out a comparative study, through numerical tests, between the new method and existing methods, namely HS, WYL, and SFA, using Wolfe's inexact line search. The results obtained show that the new method outperforms the considered methods in terms of performance and efficiency. Note de contenu : Introduction 3 1 Fundamental concepts for unconstrained optimization 5 1.1 Unconstrained nonlinear optimization . . . . . . . . . . . . . . 5 1.1.1 Preliminary concepts . . . . . . . . . . . . . . . . . . . 5 1.1.2 The results of existence and uniqueness . . . . . . . . . 8 1.1.3 Optimality conditions . . . . . . . . . . . . . . . . . . 9 1.2 Descent methods . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2.1 The principal of descent methods . . . . . . . . . . . . 10 1.2.2 Gradient method . . . . . . . . . . . . . . . . . . . . . 11 1.2.3 Newton Method . . . . . . . . . . . . . . . . . . . . . . 13 1.2.4 Quasi-Newton methods . . . . . . . . . . . . . . . . . . 15 1.2.5 Relaxation method . . . . . . . . . . . . . . . . . . . . 17 2 Line search techniques and conjugate gradient method 19 2.1 Line search methods . . . . . . . . . . . . . . . . . . . . . . . 19 2.1.1 The line search principle . . . . . . . . . . . . . . . . . 19 2.1.2 Exact line search . . . . . . . . . . . . . . . . . . . . . 20 2.1.3 Inexact line search . . . . . . . . . . . . . . . . . . . . 21 2.2 Conjugate gradient methods . . . . . . . . . . . . . . . . . . . 25 2.2.1 Conjugate gradient method for the linear case . . . . . 25 2.2.2 Conjugate gradient method for the nonlinear case . . . 28 2.3 Convergence results of the conjugate gradient method . . . . . 32 2.3.1 Conditions C1 and C2 and Zoutendijk’s Theorem . . . 32 2.3.2 Zoutendijk’s Theorem and global convergence . . . . . 33 3 New variant of the type WYL conjugate gradient method 35 3.1 New variant of the type WYL conjugate gradient method . . . 35 3.2 The sufficient descent property . . . . . . . . . . . . . . . . . . 38 3.3 Global convergence properties . . . . . . . . . . . . . . . . . . 39 3.4 Numerical experiments . . . . . . . . . . . . . . . . . . . . . . 40 3.4.1 Commentaries . . . . . . . . . . . . . . . . . . . . . . . 47 Conclusion 48 Bibliography 49 Côte titre : MAM/0778 New Variant Of The Conjugate Gradient Method With Practical Application [texte imprimé] / Malika Kerour, Auteur ; Hanaa Hemissi, Auteur ; Khelladi ,Samia, Directeur de thèse . - [S.l.] : Sétif:UFA1, 2025 . - 1 vol (49 f.) ; 29 cm. Langues : Anglais (eng) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Nonlinear unconstrained optimization Conjugate gradient method Descent direction Global convergence Inexact line search Index. décimale : 510-Mathématique Résumé : Abstract The conjugate gradient method is one of the most effective methods for solving unconstrained nonlinear optimization problems, as well as for solving large dimensional linear systems. In this dissertation, we propose a new conjugate gradient method, characterized by an improved descent direction and a new WYL-type parameter, denoted YHS, followed by a comprehensive theoretical study. We carried out a comparative study, through numerical tests, between the new method and existing methods, namely HS, WYL, and SFA, using Wolfe's inexact line search. The results obtained show that the new method outperforms the considered methods in terms of performance and efficiency. Note de contenu : Introduction 3 1 Fundamental concepts for unconstrained optimization 5 1.1 Unconstrained nonlinear optimization . . . . . . . . . . . . . . 5 1.1.1 Preliminary concepts . . . . . . . . . . . . . . . . . . . 5 1.1.2 The results of existence and uniqueness . . . . . . . . . 8 1.1.3 Optimality conditions . . . . . . . . . . . . . . . . . . 9 1.2 Descent methods . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2.1 The principal of descent methods . . . . . . . . . . . . 10 1.2.2 Gradient method . . . . . . . . . . . . . . . . . . . . . 11 1.2.3 Newton Method . . . . . . . . . . . . . . . . . . . . . . 13 1.2.4 Quasi-Newton methods . . . . . . . . . . . . . . . . . . 15 1.2.5 Relaxation method . . . . . . . . . . . . . . . . . . . . 17 2 Line search techniques and conjugate gradient method 19 2.1 Line search methods . . . . . . . . . . . . . . . . . . . . . . . 19 2.1.1 The line search principle . . . . . . . . . . . . . . . . . 19 2.1.2 Exact line search . . . . . . . . . . . . . . . . . . . . . 20 2.1.3 Inexact line search . . . . . . . . . . . . . . . . . . . . 21 2.2 Conjugate gradient methods . . . . . . . . . . . . . . . . . . . 25 2.2.1 Conjugate gradient method for the linear case . . . . . 25 2.2.2 Conjugate gradient method for the nonlinear case . . . 28 2.3 Convergence results of the conjugate gradient method . . . . . 32 2.3.1 Conditions C1 and C2 and Zoutendijk’s Theorem . . . 32 2.3.2 Zoutendijk’s Theorem and global convergence . . . . . 33 3 New variant of the type WYL conjugate gradient method 35 3.1 New variant of the type WYL conjugate gradient method . . . 35 3.2 The sufficient descent property . . . . . . . . . . . . . . . . . . 38 3.3 Global convergence properties . . . . . . . . . . . . . . . . . . 39 3.4 Numerical experiments . . . . . . . . . . . . . . . . . . . . . . 40 3.4.1 Commentaries . . . . . . . . . . . . . . . . . . . . . . . 47 Conclusion 48 Bibliography 49 Côte titre : MAM/0778

Exemplaires (1)

Code-barres	Cote	Support	Localisation	Section	Disponibilité
MAM/0778	MAM/0778	Mémoire	Bibliothèque des sciences	Anglais	Disponible Disponible

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