University Sétif 1 FERHAT ABBAS Faculty of Sciences
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Auteur Zakia Nour El Houda Begag |
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Ajouter le résultat dans votre panier Affiner la rechercheA full-Newton step interior-point method based on a class of specific equivalent algebric transformation for convex quadratic programming / Zakia Nour El Houda Begag
Titre : A full-Newton step interior-point method based on a class of specific equivalent algebric transformation for convex quadratic programming Type de document : texte imprimé Auteurs : Zakia Nour El Houda Begag, Auteur ; Slimane Hebbache ; Samia Kettab, Directeur de thèse Editeur : Sétif:UFS Année de publication : 2024 Importance : 1 vol (f.) Format : 29 cm Langues : Anglais (eng) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Convex quadratic programming
Interior point methods
Algebraic equivalent transformation
Polynomial complexityIndex. décimale : 510-Mathématique Résumé :
In this dissertation, we are interested in the theoretical and numerical study of feasible path-following interior point methods of primal-dual type to solving convex quadratic programming problems which based on new directions. The latter is obtained via the application of algebraically equivalent transformations on the equations which characterizes the central-path. Under some appropriate conditions, the corresponding algorithm is welldefined and converges quadratically to an optimal solution of the convex quadratic programming. In addition, this algorithm with short-step admits the best polynomial complexity. Finally, this dissertation is ended by presenting some numerical results to show its efficiency.Note de contenu : Sommaire
Introduction2
1 ConvexanalysisandQuadraticprogramming4
1.1 Convexanalysisreminder........................ 4
1.1.1 Convexsetsandfunctions.................... 4
1.1.2 Characterizationofadifferentiableconvexfunction...... 5
1.2 Mathematicalprogramming....................... 6
1.2.1 Existenceanduniquenessofanoptimalsolution........ 7
1.2.2 Classificationofamathematicalprogram............ 8
1.2.3 Qualificationofconstraints.................... 8
1.2.4 Solvingamathematicalprogram................ 9
1.2.5 Optimalconditions........................ 9
1.3 Convexquadraticprogrammingformula(CQP)............ 10
1.3.1 Primalconvexquadraticproblem................ 11
1.3.2 Dualconvexquadraticproblem................. 11
1.3.3 Existenceanduniquenessofasolution............. 12
1.3.4 Optimalityconditions...................... 12
1.3.5 Propertiesofduality....................... 12
1.4 Newton-Raphsonmethodforanonlinearsystem............ 13
1.5 Methodsforsolvinga(CQP)...................... 14
1.6 Central-pathmethod........................... 15
1.6.1 Descriptionofthemethod.................... 15
1.6.2 Researchdirections....................... 17
1.6.3 Genericprimaldualcentraltrajectoryalgorithmfor(CQP) 19
1.6.4 Convergenceofthealgorithm:................. 19
2 Afeasibleprimal-dualinterior-pointmethodbasedonclassofspe-
cific algebratransformation21
2.1 Newsearchdirections.......................... 21
2.2 TheAlgorithm.............................. 26
2.3 Complexityanalysisofthealgorithm.................. 27
3 Numericalresults32
3.1 Exampleswithfixedsize......................... 32
3.2 Examplewithvariablesize........................ 35
3.3 Numericalresultswiththeoreticalchoiceof θ with fixedsize..... 37
3.4 Numericalresultswiththeoreticalchoiceof θ with variablesize.... 39
3.5 Ameliortednumericalresults....................... 40Côte titre : MAM/0719 A full-Newton step interior-point method based on a class of specific equivalent algebric transformation for convex quadratic programming [texte imprimé] / Zakia Nour El Houda Begag, Auteur ; Slimane Hebbache ; Samia Kettab, Directeur de thèse . - [S.l.] : Sétif:UFS, 2024 . - 1 vol (f.) ; 29 cm.
Langues : Anglais (eng)
Catégories : Thèses & Mémoires:Mathématique Mots-clés : Convex quadratic programming
Interior point methods
Algebraic equivalent transformation
Polynomial complexityIndex. décimale : 510-Mathématique Résumé :
In this dissertation, we are interested in the theoretical and numerical study of feasible path-following interior point methods of primal-dual type to solving convex quadratic programming problems which based on new directions. The latter is obtained via the application of algebraically equivalent transformations on the equations which characterizes the central-path. Under some appropriate conditions, the corresponding algorithm is welldefined and converges quadratically to an optimal solution of the convex quadratic programming. In addition, this algorithm with short-step admits the best polynomial complexity. Finally, this dissertation is ended by presenting some numerical results to show its efficiency.Note de contenu : Sommaire
Introduction2
1 ConvexanalysisandQuadraticprogramming4
1.1 Convexanalysisreminder........................ 4
1.1.1 Convexsetsandfunctions.................... 4
1.1.2 Characterizationofadifferentiableconvexfunction...... 5
1.2 Mathematicalprogramming....................... 6
1.2.1 Existenceanduniquenessofanoptimalsolution........ 7
1.2.2 Classificationofamathematicalprogram............ 8
1.2.3 Qualificationofconstraints.................... 8
1.2.4 Solvingamathematicalprogram................ 9
1.2.5 Optimalconditions........................ 9
1.3 Convexquadraticprogrammingformula(CQP)............ 10
1.3.1 Primalconvexquadraticproblem................ 11
1.3.2 Dualconvexquadraticproblem................. 11
1.3.3 Existenceanduniquenessofasolution............. 12
1.3.4 Optimalityconditions...................... 12
1.3.5 Propertiesofduality....................... 12
1.4 Newton-Raphsonmethodforanonlinearsystem............ 13
1.5 Methodsforsolvinga(CQP)...................... 14
1.6 Central-pathmethod........................... 15
1.6.1 Descriptionofthemethod.................... 15
1.6.2 Researchdirections....................... 17
1.6.3 Genericprimaldualcentraltrajectoryalgorithmfor(CQP) 19
1.6.4 Convergenceofthealgorithm:................. 19
2 Afeasibleprimal-dualinterior-pointmethodbasedonclassofspe-
cific algebratransformation21
2.1 Newsearchdirections.......................... 21
2.2 TheAlgorithm.............................. 26
2.3 Complexityanalysisofthealgorithm.................. 27
3 Numericalresults32
3.1 Exampleswithfixedsize......................... 32
3.2 Examplewithvariablesize........................ 35
3.3 Numericalresultswiththeoreticalchoiceof θ with fixedsize..... 37
3.4 Numericalresultswiththeoreticalchoiceof θ with variablesize.... 39
3.5 Ameliortednumericalresults....................... 40Côte titre : MAM/0719 Exemplaires
Code-barres Cote Support Localisation Section Disponibilité aucun exemplaire
Titre : A full-Newton step interior-point method based on a class of specific equivalent algebric transformation for convex quadratic programming Type de document : texte imprimé Auteurs : Zakia Nour El Houda Begag, Auteur ; Slimane Hebbache ; Samia Kettab, Directeur de thèse Editeur : Sétif:UFS Année de publication : 2024 Importance : 1 vol (f.) Format : 29 cm Langues : Anglais (eng) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Convex quadratic programming
Interior point methods
Algebraic equivalent transformation
Polynomial complexityIndex. décimale : 510-Mathématique Résumé :
In this dissertation, we are interested in the theoretical and numerical study of feasible path-following interior point methods of primal-dual type to solving convex quadratic programming problems which based on new directions. The latter is obtained via the application of algebraically equivalent transformations on the equations which characterizes the central-path. Under some appropriate conditions, the corresponding algorithm is welldefined and converges quadratically to an optimal solution of the convex quadratic programming. In addition, this algorithm with short-step admits the best polynomial complexity. Finally, this dissertation is ended by presenting some numerical results to show its efficiency.Note de contenu : Sommaire
Introduction2
1 ConvexanalysisandQuadraticprogramming4
1.1 Convexanalysisreminder........................ 4
1.1.1 Convexsetsandfunctions.................... 4
1.1.2 Characterizationofadifferentiableconvexfunction...... 5
1.2 Mathematicalprogramming....................... 6
1.2.1 Existenceanduniquenessofanoptimalsolution........ 7
1.2.2 Classificationofamathematicalprogram............ 8
1.2.3 Qualificationofconstraints.................... 8
1.2.4 Solvingamathematicalprogram................ 9
1.2.5 Optimalconditions........................ 9
1.3 Convexquadraticprogrammingformula(CQP)............ 10
1.3.1 Primalconvexquadraticproblem................ 11
1.3.2 Dualconvexquadraticproblem................. 11
1.3.3 Existenceanduniquenessofasolution............. 12
1.3.4 Optimalityconditions...................... 12
1.3.5 Propertiesofduality....................... 12
1.4 Newton-Raphsonmethodforanonlinearsystem............ 13
1.5 Methodsforsolvinga(CQP)...................... 14
1.6 Central-pathmethod........................... 15
1.6.1 Descriptionofthemethod.................... 15
1.6.2 Researchdirections....................... 17
1.6.3 Genericprimaldualcentraltrajectoryalgorithmfor(CQP) 19
1.6.4 Convergenceofthealgorithm:................. 19
2 Afeasibleprimal-dualinterior-pointmethodbasedonclassofspe-
cific algebratransformation21
2.1 Newsearchdirections.......................... 21
2.2 TheAlgorithm.............................. 26
2.3 Complexityanalysisofthealgorithm.................. 27
3 Numericalresults32
3.1 Exampleswithfixedsize......................... 32
3.2 Examplewithvariablesize........................ 35
3.3 Numericalresultswiththeoreticalchoiceof θ with fixedsize..... 37
3.4 Numericalresultswiththeoreticalchoiceof θ with variablesize.... 39
3.5 Ameliortednumericalresults....................... 40Côte titre : MAM/0719 A full-Newton step interior-point method based on a class of specific equivalent algebric transformation for convex quadratic programming [texte imprimé] / Zakia Nour El Houda Begag, Auteur ; Slimane Hebbache ; Samia Kettab, Directeur de thèse . - [S.l.] : Sétif:UFS, 2024 . - 1 vol (f.) ; 29 cm.
Langues : Anglais (eng)
Catégories : Thèses & Mémoires:Mathématique Mots-clés : Convex quadratic programming
Interior point methods
Algebraic equivalent transformation
Polynomial complexityIndex. décimale : 510-Mathématique Résumé :
In this dissertation, we are interested in the theoretical and numerical study of feasible path-following interior point methods of primal-dual type to solving convex quadratic programming problems which based on new directions. The latter is obtained via the application of algebraically equivalent transformations on the equations which characterizes the central-path. Under some appropriate conditions, the corresponding algorithm is welldefined and converges quadratically to an optimal solution of the convex quadratic programming. In addition, this algorithm with short-step admits the best polynomial complexity. Finally, this dissertation is ended by presenting some numerical results to show its efficiency.Note de contenu : Sommaire
Introduction2
1 ConvexanalysisandQuadraticprogramming4
1.1 Convexanalysisreminder........................ 4
1.1.1 Convexsetsandfunctions.................... 4
1.1.2 Characterizationofadifferentiableconvexfunction...... 5
1.2 Mathematicalprogramming....................... 6
1.2.1 Existenceanduniquenessofanoptimalsolution........ 7
1.2.2 Classificationofamathematicalprogram............ 8
1.2.3 Qualificationofconstraints.................... 8
1.2.4 Solvingamathematicalprogram................ 9
1.2.5 Optimalconditions........................ 9
1.3 Convexquadraticprogrammingformula(CQP)............ 10
1.3.1 Primalconvexquadraticproblem................ 11
1.3.2 Dualconvexquadraticproblem................. 11
1.3.3 Existenceanduniquenessofasolution............. 12
1.3.4 Optimalityconditions...................... 12
1.3.5 Propertiesofduality....................... 12
1.4 Newton-Raphsonmethodforanonlinearsystem............ 13
1.5 Methodsforsolvinga(CQP)...................... 14
1.6 Central-pathmethod........................... 15
1.6.1 Descriptionofthemethod.................... 15
1.6.2 Researchdirections....................... 17
1.6.3 Genericprimaldualcentraltrajectoryalgorithmfor(CQP) 19
1.6.4 Convergenceofthealgorithm:................. 19
2 Afeasibleprimal-dualinterior-pointmethodbasedonclassofspe-
cific algebratransformation21
2.1 Newsearchdirections.......................... 21
2.2 TheAlgorithm.............................. 26
2.3 Complexityanalysisofthealgorithm.................. 27
3 Numericalresults32
3.1 Exampleswithfixedsize......................... 32
3.2 Examplewithvariablesize........................ 35
3.3 Numericalresultswiththeoreticalchoiceof θ with fixedsize..... 37
3.4 Numericalresultswiththeoreticalchoiceof θ with variablesize.... 39
3.5 Ameliortednumericalresults....................... 40Côte titre : MAM/0719 Exemplaires (1)
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