University Sétif 1 FERHAT ABBAS Faculty of Sciences
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Auteur Hasna Roubeche |
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Ajouter le résultat dans votre panier Affiner la rechercheSolving general absolute value equations via the horizontal linear complementarity problem and interior-point methods / Bouthaina Mayouf
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 methodsIndex. 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................................28Côte 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 methodsIndex. 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................................28Côte titre : MAM/0723 Exemplaires
Code-barres Cote Support Localisation Section Disponibilité aucun exemplaire
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 methodsIndex. 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................................28Côte 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 methodsIndex. 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................................28Côte titre : MAM/0723 Exemplaires (1)
Code-barres Cote Support Localisation Section Disponibilité MAM/0723 MAM/0723 Mémoire Bibliothéque des sciences Anglais Disponible
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