Solving general absolute value equations via the horizontal linear complementarity problem and interior-point methods / Bouthaina Mayouf

Public ISBD 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

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Solving general absolute value equations via the horizontal linear complementarity problem and interior-point methods / Bouthaina Mayouf  

Public ISBD Titre : Solving general absolute value equations via the horizontal linear complementarity problem and interior-point methods Type de document : document électronique 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 En ligne : http://dspace.univ-setif.dz:8888/jspui/bitstream/123456789/5444/1/mam0723.pdf Solving general absolute value equations via the horizontal linear complementarity problem and interior-point methods [document électronique] / 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 En ligne : http://dspace.univ-setif.dz:8888/jspui/bitstream/123456789/5444/1/mam0723.pdf

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