Titre :	Solving general absolute value equations via the horizontal linear complementarity problem and interior-point methods
Type de document :	texte imprimé
Auteurs :	Bouthaina Mayouf, Auteur ; Hasna Roubeche ; Hazzam,nadia, Directeur de thèse
Editeur :	Sétif:UFS
Année de publication :	2024
Importance :	1 vol (31 f.)
Format :	29 cm
Langues :	Anglais (eng)
Catégories :	Thèses & Mémoires:Mathématique
Mots-clés :	General absolute value equation Horizontal linear complementarity problem Infeasible interior point methods
Index. décimale :	510-Mathématique
Résumé :	In this work, we focus on theoretical and numerical study to solve the general absolute value equation. First, we present the transformation of this equation into a horizontal linear complementarity problem. Then, to solve the equation, we present an infeasible primal dual interior point method using the complementarity problem. This work is accompanied by numerical results.
Note de contenu :	Sommaire 1 Preliminaries9 1.1 MatrixAnalysis..................................9 1.1.1 SymmetricMatrix............................9 1.1.2 PrincipalMinors.............................9 1.1.3 InvertibleMatrix.............................9 1.1.4 VectorNorm...............................10 1.1.5 Matrixnorm...............................10 1.1.6 Eigenvalueofamatrix..........................11 1.1.7 Singularvalueofamatrix........................11 1.2 LinearComplementarityProblem........................11 1.2.1 Mathematicalformulation........................11 1.2.2 ClassesofLCP..............................12 1.2.3 ExistenceofasolutionofLCP......................12 1.3 ResolutionmethodsforLCP...........................13 1.3.1 Lemke’smethod.............................13 1.3.2 InteriorPointmethod...........................13 1.4 Horizontallinearcomplementarityproblem...................15 1.4.1 ClassesofHLCP.............................16 2 GeneralizedAbsoluteValueEquation(GAVE)17 2.1 Mathematicalframework.............................17 2.2 Existenceanduniquenessofthesolutionof GAVE . ..............18 2.3 ReformulationoftheGAVEasanHLCP.....................18 2.4 Infeasiblecentral-pathfollowinginteriorpointmethodforHLCP........19 2.4.1 Central-pathofHLCP..........................20 2.4.2 Newton’sdirections...........................21 2.4.3 Step-size.................................22 2.4.4 Algorithm.................................22 3 Numericalresults24 3.1 Examples.....................................24 3.1.1 Comments................................28
Côte titre :	MAM/0723

Solving general absolute value equations via the horizontal linear complementarity problem and interior-point methods [texte imprimé] / Bouthaina Mayouf, Auteur ; Hasna Roubeche ; Hazzam,nadia, Directeur de thèse . - [S.l.] : Sétif:UFS, 2024 . - 1 vol (31 f.) ; 29 cm.
Langues : Anglais (eng)

Catégories :	Thèses & Mémoires:Mathématique
Mots-clés :	General absolute value equation Horizontal linear complementarity problem Infeasible interior point methods
Index. décimale :	510-Mathématique
Résumé :	In this work, we focus on theoretical and numerical study to solve the general absolute value equation. First, we present the transformation of this equation into a horizontal linear complementarity problem. Then, to solve the equation, we present an infeasible primal dual interior point method using the complementarity problem. This work is accompanied by numerical results.
Note de contenu :	Sommaire 1 Preliminaries9 1.1 MatrixAnalysis..................................9 1.1.1 SymmetricMatrix............................9 1.1.2 PrincipalMinors.............................9 1.1.3 InvertibleMatrix.............................9 1.1.4 VectorNorm...............................10 1.1.5 Matrixnorm...............................10 1.1.6 Eigenvalueofamatrix..........................11 1.1.7 Singularvalueofamatrix........................11 1.2 LinearComplementarityProblem........................11 1.2.1 Mathematicalformulation........................11 1.2.2 ClassesofLCP..............................12 1.2.3 ExistenceofasolutionofLCP......................12 1.3 ResolutionmethodsforLCP...........................13 1.3.1 Lemke’smethod.............................13 1.3.2 InteriorPointmethod...........................13 1.4 Horizontallinearcomplementarityproblem...................15 1.4.1 ClassesofHLCP.............................16 2 GeneralizedAbsoluteValueEquation(GAVE)17 2.1 Mathematicalframework.............................17 2.2 Existenceanduniquenessofthesolutionof GAVE . ..............18 2.3 ReformulationoftheGAVEasanHLCP.....................18 2.4 Infeasiblecentral-pathfollowinginteriorpointmethodforHLCP........19 2.4.1 Central-pathofHLCP..........................20 2.4.2 Newton’sdirections...........................21 2.4.3 Step-size.................................22 2.4.4 Algorithm.................................22 3 Numericalresults24 3.1 Examples.....................................24 3.1.1 Comments................................28
Côte titre :	MAM/0723