Titre :	Newton-Raphson method and arithmetic mean Newton’s method for weighted linear complementarity problems
Type de document :	texte imprimé
Auteurs :	Assala Chouchane, Auteur ; Khaled Kamel ; Mohamed Achache, Directeur de thèse
Editeur :	Sétif:UFS
Année de publication :	2024
Importance :	1 vol (48 f.)
Format :	29 cm
Langues :	Anglais (eng)
Catégories :	Thèses & Mémoires:Mathématique
Mots-clés :	Weighted linear complementarity problem Newton-Raphson method Quadratic convergence
Index. décimale :	510-Mathématique
Résumé :	The goal of this thesis is to solve weighted linear complementarity problems. To do this, we first formulate the latter in the form of an equivalent system of nonlinear equations. We then applied the Newton-Raphson method to solve it. Under certain conditions, we prove the local quadratic convergence of this method to the unique solution. The numerical results obtained confirm the effectiveness of this method. Furthermore, to accelerate the convergence and improve the first method, we introduce the Newton arithmetic mean method. The numerical results obtained are very encouraging. Finally, we end this thesis with a conclusion and perspectives.
Note de contenu :	Sommaire 1 Introduction 4 1.1 Dissertation organization . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Terminology and notation . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Preliminaries 8 2.1 Matrix and di¤erential calculus . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 A system of nonlinear equations in Rn . . . . . . . . . . . . . . . . . . . 12 2.2.1 A Newton-Raphson method for solving F(x) = 0Rn . . . . . . . . 13 2.2.2 Convergence analysis of NewtonÂ’s method for solving F(x) = 0Rn: 15 2.3 Standard LCP and methods of its resolution . . . . . . . . . . . . . . . . 17 2.3.1 Standard linear complementarity problems . . . . . . . . . . . . . 17 2.3.2 Classes of linear complementarity problems . . . . . . . . . . . . . 18 2.3.3 LCP and optimization problems . . . . . . . . . . . . . . . . . . . 20 2.3.4 Resolution methods of LCP . . . . . . . . . . . . . . . . . . . . . 21 3 The Newton-Raphson method for solving wLCP 24 3.1 The Newton-Raphson method for wLCP . . . . . . . . . . . . . . . . . . 25 3.1.1 The Newton-Raphson iteration method . . . . . . . . . . . . . . . 25 3.1.2 The Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.1.3 Convergence analysis . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 Numerical experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2.1 Numerical results with Newton-Raphson method . . . . . . . . . 31 4 The Arithmetic Mean NewtonÂ’s method for solving wLCP 37 4.1 The principle of the proposed method . . . . . . . . . . . . . . . . . . . . 37 4.2 Arithmetic Mean NewtonÂ’s method for solving the weighted LCP . . . . 39 4.2.1 The Algorithm of Arithmetic Mean NewtonÂ’s method . . . . . . . 41 4.2.2 Numerical experiments with Alg AMN and comparison . . . . . . 43 4.3 Conclusion and future remarks . . . . . . . . . . . . . . . . . . . . . . . . 45
Côte titre :	MAM/0715

Newton-Raphson method and arithmetic mean Newton’s method for weighted linear complementarity problems [texte imprimé] / Assala Chouchane, Auteur ; Khaled Kamel ; Mohamed Achache, Directeur de thèse . - [S.l.] : Sétif:UFS, 2024 . - 1 vol (48 f.) ; 29 cm.
Langues : Anglais (eng)

Catégories :	Thèses & Mémoires:Mathématique
Mots-clés :	Weighted linear complementarity problem Newton-Raphson method Quadratic convergence
Index. décimale :	510-Mathématique
Résumé :	The goal of this thesis is to solve weighted linear complementarity problems. To do this, we first formulate the latter in the form of an equivalent system of nonlinear equations. We then applied the Newton-Raphson method to solve it. Under certain conditions, we prove the local quadratic convergence of this method to the unique solution. The numerical results obtained confirm the effectiveness of this method. Furthermore, to accelerate the convergence and improve the first method, we introduce the Newton arithmetic mean method. The numerical results obtained are very encouraging. Finally, we end this thesis with a conclusion and perspectives.
Note de contenu :	Sommaire 1 Introduction 4 1.1 Dissertation organization . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Terminology and notation . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Preliminaries 8 2.1 Matrix and di¤erential calculus . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 A system of nonlinear equations in Rn . . . . . . . . . . . . . . . . . . . 12 2.2.1 A Newton-Raphson method for solving F(x) = 0Rn . . . . . . . . 13 2.2.2 Convergence analysis of NewtonÂ’s method for solving F(x) = 0Rn: 15 2.3 Standard LCP and methods of its resolution . . . . . . . . . . . . . . . . 17 2.3.1 Standard linear complementarity problems . . . . . . . . . . . . . 17 2.3.2 Classes of linear complementarity problems . . . . . . . . . . . . . 18 2.3.3 LCP and optimization problems . . . . . . . . . . . . . . . . . . . 20 2.3.4 Resolution methods of LCP . . . . . . . . . . . . . . . . . . . . . 21 3 The Newton-Raphson method for solving wLCP 24 3.1 The Newton-Raphson method for wLCP . . . . . . . . . . . . . . . . . . 25 3.1.1 The Newton-Raphson iteration method . . . . . . . . . . . . . . . 25 3.1.2 The Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.1.3 Convergence analysis . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 Numerical experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2.1 Numerical results with Newton-Raphson method . . . . . . . . . 31 4 The Arithmetic Mean NewtonÂ’s method for solving wLCP 37 4.1 The principle of the proposed method . . . . . . . . . . . . . . . . . . . . 37 4.2 Arithmetic Mean NewtonÂ’s method for solving the weighted LCP . . . . 39 4.2.1 The Algorithm of Arithmetic Mean NewtonÂ’s method . . . . . . . 41 4.2.2 Numerical experiments with Alg AMN and comparison . . . . . . 43 4.3 Conclusion and future remarks . . . . . . . . . . . . . . . . . . . . . . . . 45
Côte titre :	MAM/0715