Developing an Interior Point Method for Convex Quadratic Programming / Lina Tesslim Sinacer  

Public ISBD Titre : Developing an Interior Point Method for Convex Quadratic Programming Type de document : document électronique Auteurs : Lina Tesslim Sinacer, Auteur ; Rania Grachi, Auteur ; Goutali, Moufida, Directeur de thèse Editeur : Sétif:UFS Année de publication : 2025 Importance : 1 vol (47 f.) Format : 29 cm Langues : Anglais (eng) Mots-clés : Convex Quadratic Programming Algebraic Transformation Centrality Condition Search Direction Convergence Analysis Complexity Analysis Numerical Experiments Résumé : This thesis deal with the development of a primal-dual interior-point method for solving convex quadratic programming problems. The proposed approach is based on an algebraic transformation of the centrality condition in order to derive a new search direction that improves the efficiency and numerical performance of the algorithm. The theoretical properties of the method are investigated through convergence and computational complexity analyses. In addition, numerical experiments are conducted on a set of benchmark problems. The obtained results demonstrate that the proposed method efficiently reaches the optimal solution with a small number of iterations and satisfactory computational performance, confirming its effectiveness for solving convex quadratic programming problems. Note de contenu : Contents Glossary of Notation 8 Introduction 11 1 Convex Analysis and Mathematical Programming 14 1.1 Basic Elements of Convex Analysis . . . . . . . . . . . . . . . . . . . . . . 14 1.2 Mathematical Programming . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.2.1 Local and Global Optimal Solutions . . . . . . . . . . . . . . . . . 16 1.2.2 Classification of mathematical programs . . . . . . . . . . . . . . 17 1.2.3 Qualification of constraints . . . . . . . . . . . . . . . . . . . . . . 17 1.3 Solving Mathematical Programming Problems . . . . . . . . . . . . . . . 18 1.3.1 Existence and Uniqueness of Optimal Solutions . . . . . . . . . . 18 1.3.2 Optimality Conditions . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.4 Newton’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.5 Convex Quadratic Programming . . . . . . . . . . . . . . . . . . . . . . . 20 1.5.1 Solution Methods for Convex Quadratic Optimization . . . . . . 21 1.5.2 Perturbed Problem (Logarithmic Barrier) . . . . . . . . . . . . . . 21 2 A New Short-Step IPA for Convex Quadratic Optimization 23 2.1 The new search direction for CQO by using AET . . . . . . . . . . . . . . 24 2.1.1 The Proximity Measure . . . . . . . . . . . . . . . . . . . . . . . . 26 2.1.2 Primal–Dual IP Algorithm for CQO . . . . . . . . . . . . . . . . . 27 2.2 Convergence Behavior and Computational Complexity of the Proposed Algorithm . . 28 2.2.1 Preliminary Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.2.2 Feasibility Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.2.3 Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3 Numerical experimentation 37 3.1 Examples with fixed size . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.1.1 Results of Examples (Table (3.1)) . . . . . . . . . . . . . . . . . . . 41 3.2 Example with variable size . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.2.1 Results of Example (Table (3.2)) . . . . . . . . . . . . . . . . . . . . 43 3.3 Discussion of Numerical Results . . . . . . . . . . . . . . . . . . . . . . . 44 Conclusion 45 Bibliography 46 Côte titre : MAM/0849 En ligne : https://repository.univ-setif.dz/server/api/core/bitstreams/371bdd13-f54d-4023-b [...] Developing an Interior Point Method for Convex Quadratic Programming [document électronique] / Lina Tesslim Sinacer, Auteur ; Rania Grachi, Auteur ; Goutali, Moufida, Directeur de thèse . - [S.l.] : Sétif:UFS, 2025 . - 1 vol (47 f.) ; 29 cm. Langues : Anglais (eng) Mots-clés : Convex Quadratic Programming Algebraic Transformation Centrality Condition Search Direction Convergence Analysis Complexity Analysis Numerical Experiments Résumé : This thesis deal with the development of a primal-dual interior-point method for solving convex quadratic programming problems. The proposed approach is based on an algebraic transformation of the centrality condition in order to derive a new search direction that improves the efficiency and numerical performance of the algorithm. The theoretical properties of the method are investigated through convergence and computational complexity analyses. In addition, numerical experiments are conducted on a set of benchmark problems. The obtained results demonstrate that the proposed method efficiently reaches the optimal solution with a small number of iterations and satisfactory computational performance, confirming its effectiveness for solving convex quadratic programming problems. Note de contenu : Contents Glossary of Notation 8 Introduction 11 1 Convex Analysis and Mathematical Programming 14 1.1 Basic Elements of Convex Analysis . . . . . . . . . . . . . . . . . . . . . . 14 1.2 Mathematical Programming . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.2.1 Local and Global Optimal Solutions . . . . . . . . . . . . . . . . . 16 1.2.2 Classification of mathematical programs . . . . . . . . . . . . . . 17 1.2.3 Qualification of constraints . . . . . . . . . . . . . . . . . . . . . . 17 1.3 Solving Mathematical Programming Problems . . . . . . . . . . . . . . . 18 1.3.1 Existence and Uniqueness of Optimal Solutions . . . . . . . . . . 18 1.3.2 Optimality Conditions . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.4 Newton’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.5 Convex Quadratic Programming . . . . . . . . . . . . . . . . . . . . . . . 20 1.5.1 Solution Methods for Convex Quadratic Optimization . . . . . . 21 1.5.2 Perturbed Problem (Logarithmic Barrier) . . . . . . . . . . . . . . 21 2 A New Short-Step IPA for Convex Quadratic Optimization 23 2.1 The new search direction for CQO by using AET . . . . . . . . . . . . . . 24 2.1.1 The Proximity Measure . . . . . . . . . . . . . . . . . . . . . . . . 26 2.1.2 Primal–Dual IP Algorithm for CQO . . . . . . . . . . . . . . . . . 27 2.2 Convergence Behavior and Computational Complexity of the Proposed Algorithm . . 28 2.2.1 Preliminary Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.2.2 Feasibility Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.2.3 Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3 Numerical experimentation 37 3.1 Examples with fixed size . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.1.1 Results of Examples (Table (3.1)) . . . . . . . . . . . . . . . . . . . 41 3.2 Example with variable size . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.2.1 Results of Example (Table (3.2)) . . . . . . . . . . . . . . . . . . . . 43 3.3 Discussion of Numerical Results . . . . . . . . . . . . . . . . . . . . . . . 44 Conclusion 45 Bibliography 46 Côte titre : MAM/0849 En ligne : https://repository.univ-setif.dz/server/api/core/bitstreams/371bdd13-f54d-4023-b [...]

Exemplaires (1)

Code-barres	Cote	Support	Localisation	Section	Disponibilité
MAM/0849	MAM/0849	Mémoire	Bibliothèque des sciences	Anglais	Disponible Disponible

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