University Sétif 1 FERHAT ABBAS Faculty of Sciences
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Auteur Razika Bellaouar |
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Titre : Interior-point methods based on kernel function: theory and numerical experiments Type de document : document électronique Auteurs : Razika Bellaouar, Auteur ; Manar Dehilis, Auteur ; Louiza Derbal, Directeur de thèse Editeur : Sétif:UFS Année de publication : 2025 Importance : 1 vol (43 f.) Format : 29 cm Langues : Anglais (eng) Mots-clés : Linear programming
Interior-point method
Central path
Kernel function
Algorithm complexityRésumé : The aim of this thesis is to propose a primal-dual central-path interior-point method for solving linear programming problems, based on a new class of Newton directions together with a new proximity measure defined by a new kernel function. In this study, we present the main theoretical results related to interior-point methods and investigate the role of the kernel function in improving their performance, with particular emphasis on the convergence and complexity analysis of the proposed algorithm. Finally, numerical experiments are conducted to demonstrate the efficiency of the proposed algorithm. Note de contenu : Table of contents
Introduction 1
1 Basic concepts in convex analysis and linear programming 3
1.1 Elements of convexanalysis............................ 3
1.1.1 Differentiable convex functions...................... 5
1.2 Mathematical programming............................ 6
1.2.1 Existence and uniqueness of solutions.................. 6
1.2.2 Lagrangian duality of mathematical programming.......... 7
1.2.3 Linear programming............................ 7
1.3 Solution methods for programming problems.................. 10
1.3.1 Simplex method.............................. 10
1.3.2 Modern interior point methods...................... 11
2 Interior–point methods based on a new kernel function13
2.1 Central path method based on the logarithmic barrier method........ 13
2.1.1 Standard Newton Directions....................... 14
2.1.2 Generic primal–dual central path algorithm for linear programming 16
2.2 Kernel function and its qualification....................... 17
2.2.1 Qualification of (t) . ........................... 17
2.2.2 Analysis of algorithm complexity.................... 22
3 Numerical experiments32
3.1 Examples....................................... 32
3.2 Discussion and comments............................. 35
Conclusion 43
Côte titre : MAM/0844 En ligne : https://repository.univ-setif.dz/server/api/core/bitstreams/9ea7b353-159d-49f0-8 [...] Interior-point methods based on kernel function: theory and numerical experiments [document électronique] / Razika Bellaouar, Auteur ; Manar Dehilis, Auteur ; Louiza Derbal, Directeur de thèse . - [S.l.] : Sétif:UFS, 2025 . - 1 vol (43 f.) ; 29 cm.
Langues : Anglais (eng)
Mots-clés : Linear programming
Interior-point method
Central path
Kernel function
Algorithm complexityRésumé : The aim of this thesis is to propose a primal-dual central-path interior-point method for solving linear programming problems, based on a new class of Newton directions together with a new proximity measure defined by a new kernel function. In this study, we present the main theoretical results related to interior-point methods and investigate the role of the kernel function in improving their performance, with particular emphasis on the convergence and complexity analysis of the proposed algorithm. Finally, numerical experiments are conducted to demonstrate the efficiency of the proposed algorithm. Note de contenu : Table of contents
Introduction 1
1 Basic concepts in convex analysis and linear programming 3
1.1 Elements of convexanalysis............................ 3
1.1.1 Differentiable convex functions...................... 5
1.2 Mathematical programming............................ 6
1.2.1 Existence and uniqueness of solutions.................. 6
1.2.2 Lagrangian duality of mathematical programming.......... 7
1.2.3 Linear programming............................ 7
1.3 Solution methods for programming problems.................. 10
1.3.1 Simplex method.............................. 10
1.3.2 Modern interior point methods...................... 11
2 Interior–point methods based on a new kernel function13
2.1 Central path method based on the logarithmic barrier method........ 13
2.1.1 Standard Newton Directions....................... 14
2.1.2 Generic primal–dual central path algorithm for linear programming 16
2.2 Kernel function and its qualification....................... 17
2.2.1 Qualification of (t) . ........................... 17
2.2.2 Analysis of algorithm complexity.................... 22
3 Numerical experiments32
3.1 Examples....................................... 32
3.2 Discussion and comments............................. 35
Conclusion 43
Côte titre : MAM/0844 En ligne : https://repository.univ-setif.dz/server/api/core/bitstreams/9ea7b353-159d-49f0-8 [...] Exemplaires (1)
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