University Sétif 1 FERHAT ABBAS Faculty of Sciences
Détail de l'auteur
Auteur Sarra Benfriha |
Documents disponibles écrits par cet auteur
Ajouter le résultat dans votre panier Affiner la recherche
Titre : EXTENSION OF INTERIOR POINT METHOD FOR LINEAR PROGRAMMING Type de document : texte imprimé Auteurs : Sarra Benfriha, Auteur ; Manal Benlamri ; Leulmi ,Assma, Directeur de thèse Editeur : Sétif:UFS Année de publication : 2024 Importance : 1 vol (50 f.) Format : 29 cm Langues : Anglais (eng) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Linear programming
Interior point methods
logarithmic barrier methods
Approximate functionsIndex. décimale : 510-Mathématique Résumé :
We have highlighted in our study of linear programming problem that are of great importance in
problems that mimic real life. The aim of our study is to present a theoretical, algorithmic and
numerical study of the logarithmic Barrier method for resolving Linear Programming problem (LP).
Firstly, we determine the direction by Newton’s method. Then, we establish an efficient algorithm to
compute the displacement step according to the direction with the technic of approximate functions.
We present the conceptual results that ensure the existence and uniqueness of the optimal solution
to the approximate problem of LP as well as its convergence to the optimal solution of the initial
problem. Finally, their convergence results well confirmed. The results obtained through the
numerical study allowed us to give some conclusions regarding the behavior of the proposed
approximate function to find the displacement step then, the optimal solution to the problem.Note de contenu : Sommaire
Introductionv
1 PreliminariesandFundamentals1
1.1Convexanalysis.............................1
1.1.1A¢nesetsandapplications..................1
1.1.2Convexsets...........................2
1.1.3Convexcones..........................3
1.1.4Convexfunctions........................4
1.1.5Semi-continuity.........................5
1.2Penalty(Barrier)function.......................6
2 Linearprogramming8
2.1Notionofmathematicalprogramming.................8
2.2QualiÂ…cationofconstraints.......................10
2.2.1Optimalityconditions.....................10
2.2.2Mainresultsofexistenceanduniquenessof (MP) . .....11
2.2.3Lagrangianduality........................12
2.3Generaltheoryoflinearprogramming.................12
2.3.1Usualformsofalinearprogram................13
2.3.2DualityinLinearProgramming................15
2.4Methodofsolvingalinearprogramming...............17
2.4.1Simplexmethod.........................17
2.4.2Gradientmethods........................18
2.4.3Interiorpointmethod......................18
2.4.4Linesearchmethods......................20
3 Alogarithmicbarriermethodforlinearprogrammingbasedona
newapproximatefunction
25
3.1Introduction...............................25
3.2Theoreticalaspectoftheproblem (Dr) . ...............27
3.2.1Existenceanduniquenessofthesolutionofthedisturbed
problem.............................27
3.2.2Convergenceofthedisturbedproblemtowardstheproblem
(D) when r tendstowardszero................29
3.3Numericalaspectoftheproblem (Dr) . ................29
3.3.1Calculationofthedisplacementstep tk . ...........30
3.3.2Calculationofthedi¤erentvaluesofbt . ............31
3.4approximatefunctionsof . ......................32
3.4.1Primaryapproximatefunction.................32
3.4.2Secondapproximatefunction(Anewapproximatefunction)33
3.4.3Calculationofthedisplacementstep.............34
3.4.4Algorithm............................35
4 Numericalexperimentsandcommentaries36
4.1NumericalSimulations.........................36
4.1.1Comparativetable.......................44
4.2Commentary..............................46
4.3Generalconclusionandperspection..................46
Côte titre : MAM/0725 EXTENSION OF INTERIOR POINT METHOD FOR LINEAR PROGRAMMING [texte imprimé] / Sarra Benfriha, Auteur ; Manal Benlamri ; Leulmi ,Assma, Directeur de thèse . - [S.l.] : Sétif:UFS, 2024 . - 1 vol (50 f.) ; 29 cm.
Langues : Anglais (eng)
Catégories : Thèses & Mémoires:Mathématique Mots-clés : Linear programming
Interior point methods
logarithmic barrier methods
Approximate functionsIndex. décimale : 510-Mathématique Résumé :
We have highlighted in our study of linear programming problem that are of great importance in
problems that mimic real life. The aim of our study is to present a theoretical, algorithmic and
numerical study of the logarithmic Barrier method for resolving Linear Programming problem (LP).
Firstly, we determine the direction by Newton’s method. Then, we establish an efficient algorithm to
compute the displacement step according to the direction with the technic of approximate functions.
We present the conceptual results that ensure the existence and uniqueness of the optimal solution
to the approximate problem of LP as well as its convergence to the optimal solution of the initial
problem. Finally, their convergence results well confirmed. The results obtained through the
numerical study allowed us to give some conclusions regarding the behavior of the proposed
approximate function to find the displacement step then, the optimal solution to the problem.Note de contenu : Sommaire
Introductionv
1 PreliminariesandFundamentals1
1.1Convexanalysis.............................1
1.1.1A¢nesetsandapplications..................1
1.1.2Convexsets...........................2
1.1.3Convexcones..........................3
1.1.4Convexfunctions........................4
1.1.5Semi-continuity.........................5
1.2Penalty(Barrier)function.......................6
2 Linearprogramming8
2.1Notionofmathematicalprogramming.................8
2.2QualiÂ…cationofconstraints.......................10
2.2.1Optimalityconditions.....................10
2.2.2Mainresultsofexistenceanduniquenessof (MP) . .....11
2.2.3Lagrangianduality........................12
2.3Generaltheoryoflinearprogramming.................12
2.3.1Usualformsofalinearprogram................13
2.3.2DualityinLinearProgramming................15
2.4Methodofsolvingalinearprogramming...............17
2.4.1Simplexmethod.........................17
2.4.2Gradientmethods........................18
2.4.3Interiorpointmethod......................18
2.4.4Linesearchmethods......................20
3 Alogarithmicbarriermethodforlinearprogrammingbasedona
newapproximatefunction
25
3.1Introduction...............................25
3.2Theoreticalaspectoftheproblem (Dr) . ...............27
3.2.1Existenceanduniquenessofthesolutionofthedisturbed
problem.............................27
3.2.2Convergenceofthedisturbedproblemtowardstheproblem
(D) when r tendstowardszero................29
3.3Numericalaspectoftheproblem (Dr) . ................29
3.3.1Calculationofthedisplacementstep tk . ...........30
3.3.2Calculationofthedi¤erentvaluesofbt . ............31
3.4approximatefunctionsof . ......................32
3.4.1Primaryapproximatefunction.................32
3.4.2Secondapproximatefunction(Anewapproximatefunction)33
3.4.3Calculationofthedisplacementstep.............34
3.4.4Algorithm............................35
4 Numericalexperimentsandcommentaries36
4.1NumericalSimulations.........................36
4.1.1Comparativetable.......................44
4.2Commentary..............................46
4.3Generalconclusionandperspection..................46
Côte titre : MAM/0725 Exemplaires
Code-barres Cote Support Localisation Section Disponibilité aucun exemplaire
Titre : EXTENSION OF INTERIOR POINT METHOD FOR LINEAR PROGRAMMING Type de document : texte imprimé Auteurs : Sarra Benfriha, Auteur ; Manal Benlamri ; Leulmi ,Assma, Directeur de thèse Editeur : Sétif:UFS Année de publication : 2024 Importance : 1 vol (50 f.) Format : 29 cm Langues : Anglais (eng) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Linear programming
Interior point methods
logarithmic barrier methods
Approximate functionsIndex. décimale : 510-Mathématique Résumé :
We have highlighted in our study of linear programming problem that are of great importance in
problems that mimic real life. The aim of our study is to present a theoretical, algorithmic and
numerical study of the logarithmic Barrier method for resolving Linear Programming problem (LP).
Firstly, we determine the direction by Newton’s method. Then, we establish an efficient algorithm to
compute the displacement step according to the direction with the technic of approximate functions.
We present the conceptual results that ensure the existence and uniqueness of the optimal solution
to the approximate problem of LP as well as its convergence to the optimal solution of the initial
problem. Finally, their convergence results well confirmed. The results obtained through the
numerical study allowed us to give some conclusions regarding the behavior of the proposed
approximate function to find the displacement step then, the optimal solution to the problem.Note de contenu : Sommaire
Introductionv
1 PreliminariesandFundamentals1
1.1Convexanalysis.............................1
1.1.1A¢nesetsandapplications..................1
1.1.2Convexsets...........................2
1.1.3Convexcones..........................3
1.1.4Convexfunctions........................4
1.1.5Semi-continuity.........................5
1.2Penalty(Barrier)function.......................6
2 Linearprogramming8
2.1Notionofmathematicalprogramming.................8
2.2QualiÂ…cationofconstraints.......................10
2.2.1Optimalityconditions.....................10
2.2.2Mainresultsofexistenceanduniquenessof (MP) . .....11
2.2.3Lagrangianduality........................12
2.3Generaltheoryoflinearprogramming.................12
2.3.1Usualformsofalinearprogram................13
2.3.2DualityinLinearProgramming................15
2.4Methodofsolvingalinearprogramming...............17
2.4.1Simplexmethod.........................17
2.4.2Gradientmethods........................18
2.4.3Interiorpointmethod......................18
2.4.4Linesearchmethods......................20
3 Alogarithmicbarriermethodforlinearprogrammingbasedona
newapproximatefunction
25
3.1Introduction...............................25
3.2Theoreticalaspectoftheproblem (Dr) . ...............27
3.2.1Existenceanduniquenessofthesolutionofthedisturbed
problem.............................27
3.2.2Convergenceofthedisturbedproblemtowardstheproblem
(D) when r tendstowardszero................29
3.3Numericalaspectoftheproblem (Dr) . ................29
3.3.1Calculationofthedisplacementstep tk . ...........30
3.3.2Calculationofthedi¤erentvaluesofbt . ............31
3.4approximatefunctionsof . ......................32
3.4.1Primaryapproximatefunction.................32
3.4.2Secondapproximatefunction(Anewapproximatefunction)33
3.4.3Calculationofthedisplacementstep.............34
3.4.4Algorithm............................35
4 Numericalexperimentsandcommentaries36
4.1NumericalSimulations.........................36
4.1.1Comparativetable.......................44
4.2Commentary..............................46
4.3Generalconclusionandperspection..................46
Côte titre : MAM/0725 EXTENSION OF INTERIOR POINT METHOD FOR LINEAR PROGRAMMING [texte imprimé] / Sarra Benfriha, Auteur ; Manal Benlamri ; Leulmi ,Assma, Directeur de thèse . - [S.l.] : Sétif:UFS, 2024 . - 1 vol (50 f.) ; 29 cm.
Langues : Anglais (eng)
Catégories : Thèses & Mémoires:Mathématique Mots-clés : Linear programming
Interior point methods
logarithmic barrier methods
Approximate functionsIndex. décimale : 510-Mathématique Résumé :
We have highlighted in our study of linear programming problem that are of great importance in
problems that mimic real life. The aim of our study is to present a theoretical, algorithmic and
numerical study of the logarithmic Barrier method for resolving Linear Programming problem (LP).
Firstly, we determine the direction by Newton’s method. Then, we establish an efficient algorithm to
compute the displacement step according to the direction with the technic of approximate functions.
We present the conceptual results that ensure the existence and uniqueness of the optimal solution
to the approximate problem of LP as well as its convergence to the optimal solution of the initial
problem. Finally, their convergence results well confirmed. The results obtained through the
numerical study allowed us to give some conclusions regarding the behavior of the proposed
approximate function to find the displacement step then, the optimal solution to the problem.Note de contenu : Sommaire
Introductionv
1 PreliminariesandFundamentals1
1.1Convexanalysis.............................1
1.1.1A¢nesetsandapplications..................1
1.1.2Convexsets...........................2
1.1.3Convexcones..........................3
1.1.4Convexfunctions........................4
1.1.5Semi-continuity.........................5
1.2Penalty(Barrier)function.......................6
2 Linearprogramming8
2.1Notionofmathematicalprogramming.................8
2.2QualiÂ…cationofconstraints.......................10
2.2.1Optimalityconditions.....................10
2.2.2Mainresultsofexistenceanduniquenessof (MP) . .....11
2.2.3Lagrangianduality........................12
2.3Generaltheoryoflinearprogramming.................12
2.3.1Usualformsofalinearprogram................13
2.3.2DualityinLinearProgramming................15
2.4Methodofsolvingalinearprogramming...............17
2.4.1Simplexmethod.........................17
2.4.2Gradientmethods........................18
2.4.3Interiorpointmethod......................18
2.4.4Linesearchmethods......................20
3 Alogarithmicbarriermethodforlinearprogrammingbasedona
newapproximatefunction
25
3.1Introduction...............................25
3.2Theoreticalaspectoftheproblem (Dr) . ...............27
3.2.1Existenceanduniquenessofthesolutionofthedisturbed
problem.............................27
3.2.2Convergenceofthedisturbedproblemtowardstheproblem
(D) when r tendstowardszero................29
3.3Numericalaspectoftheproblem (Dr) . ................29
3.3.1Calculationofthedisplacementstep tk . ...........30
3.3.2Calculationofthedi¤erentvaluesofbt . ............31
3.4approximatefunctionsof . ......................32
3.4.1Primaryapproximatefunction.................32
3.4.2Secondapproximatefunction(Anewapproximatefunction)33
3.4.3Calculationofthedisplacementstep.............34
3.4.4Algorithm............................35
4 Numericalexperimentsandcommentaries36
4.1NumericalSimulations.........................36
4.1.1Comparativetable.......................44
4.2Commentary..............................46
4.3Generalconclusionandperspection..................46
Côte titre : MAM/0725 Exemplaires (1)
Code-barres Cote Support Localisation Section Disponibilité MAM/0725 MAM/0725 Mémoire Bibliothéque des sciences Anglais Disponible
Disponible
