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 complexity
Index. 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....................... 40
Côte 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 complexity
Index. 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....................... 40
Côte titre :	MAM/0719