Titre :	Study of a cancer therapy model using Dynamic Programming Method
Type de document :	texte imprimé
Auteurs :	Islem Akkouche, Auteur ; Mohamed Hammi ; Sofiane Lamri ; Touffik Bouremani, Directeur de thèse
Editeur :	Sétif:UFS
Année de publication :	2024
Importance :	1 vol (39 f.)
Format :	29 cm
Langues :	Anglais (eng)
Catégories :	Thèses & Mémoires:Mathématique
Mots-clés :	Non-smooth analysis Autonomous optimal control problem The Dynamic Programming Algorithm Bolza Problem.
Index. décimale :	510-Mathématique
Résumé :	In this note we use a dynamic programming method to study a mathematical model of cancer. This study is based on recent results of non-differentiable analysis, applying a generalized algorithm to obtain a complete, justified and rigorous solution.
Note de contenu :	Sommaire INTRODUCTION . ................................ 1 I NONSMOOTHANALYSISANDAPPLICATIONS . ........ 4 1.1 Introduction.................................4 1.2 PreliminaryNotions.............................4 1.2.1 Di¤erentiablemappingsonsubmanifoldsof Rn . ........4 1.2.2 StratiÂ…edsetsandmapping....................8 1.3 Conesandgeneralizedderivative......................11 1.4 Monotonicityofrealfunctions.......................12 1.4.1 Generalmonotonicityresult....................13 IISUFFICIENTCONDITIONOFNONAUTONOMOUSOPTIMAL CONTROLPROBLEMS . .......................... 16 2.1 Introduction.................................16 2.2 FormulationsandclassiÂ…cationsofnon-autonomousoptimalcontrolprob- lems .....................................16 2.2.1 Non-autonomousBolzaproblemfordi¤erentialinclusions...16 2.2.2 Non-autonomousBolzaproblemparameterized.........19 2.2.3 Lagrangeoptimalcontrolproblem.................21 2.2.4 Mayeroptimalcontrolproblem..................21 2.2.5 OptimalcontrolproblemwithÂ…xedterminaltime........21 2.2.6 Minimumtimeproblem......................22 2.2.7 Problemofvariationalcalculation.................22 2.2.8 InÂ…nitehorizonoptimalcontrolproblems.............22 2.3 VeriÂ…cationTheoremsforanon-autonomousoptimalcontrolproblem.22 2.4 Generalalgorithmforsolvinganautonomousoptimalcontrolproblem25 IIISTUDYOFACANCERTHEARAPYMODELUSINGDYNAMIC PROGRAMMINGMETHOD . ...................... 29 3.1 Introduction.................................29 3.2 MathematicalModel............................29 3.2.1 Dynamicprogrammingformulation................30 3.2.2 CharacterizationoftheHamiltonian...............30 3.2.3 Setoftransversalityterminalpoints................31 3.3 GeneralizedHamiltonianÂ…eld.......................32 3.3.1 Hamiltoniansystemonthestratum Z???? . .............33 3.3.2 Generalizedcharacteristic‡ow...................36 3.4 Valuefunctionandoptimaltrajectories..................37 3.5 Conclusionandcoments...........................37
Côte titre :	MAM/0724

Study of a cancer therapy model using Dynamic Programming Method [texte imprimé] / Islem Akkouche, Auteur ; Mohamed Hammi ; Sofiane Lamri ; Touffik Bouremani, Directeur de thèse . - [S.l.] : Sétif:UFS, 2024 . - 1 vol (39 f.) ; 29 cm.
Langues : Anglais (eng)

Catégories :	Thèses & Mémoires:Mathématique
Mots-clés :	Non-smooth analysis Autonomous optimal control problem The Dynamic Programming Algorithm Bolza Problem.
Index. décimale :	510-Mathématique
Résumé :	In this note we use a dynamic programming method to study a mathematical model of cancer. This study is based on recent results of non-differentiable analysis, applying a generalized algorithm to obtain a complete, justified and rigorous solution.
Note de contenu :	Sommaire INTRODUCTION . ................................ 1 I NONSMOOTHANALYSISANDAPPLICATIONS . ........ 4 1.1 Introduction.................................4 1.2 PreliminaryNotions.............................4 1.2.1 Di¤erentiablemappingsonsubmanifoldsof Rn . ........4 1.2.2 StratiÂ…edsetsandmapping....................8 1.3 Conesandgeneralizedderivative......................11 1.4 Monotonicityofrealfunctions.......................12 1.4.1 Generalmonotonicityresult....................13 IISUFFICIENTCONDITIONOFNONAUTONOMOUSOPTIMAL CONTROLPROBLEMS . .......................... 16 2.1 Introduction.................................16 2.2 FormulationsandclassiÂ…cationsofnon-autonomousoptimalcontrolprob- lems .....................................16 2.2.1 Non-autonomousBolzaproblemfordi¤erentialinclusions...16 2.2.2 Non-autonomousBolzaproblemparameterized.........19 2.2.3 Lagrangeoptimalcontrolproblem.................21 2.2.4 Mayeroptimalcontrolproblem..................21 2.2.5 OptimalcontrolproblemwithÂ…xedterminaltime........21 2.2.6 Minimumtimeproblem......................22 2.2.7 Problemofvariationalcalculation.................22 2.2.8 InÂ…nitehorizonoptimalcontrolproblems.............22 2.3 VeriÂ…cationTheoremsforanon-autonomousoptimalcontrolproblem.22 2.4 Generalalgorithmforsolvinganautonomousoptimalcontrolproblem25 IIISTUDYOFACANCERTHEARAPYMODELUSINGDYNAMIC PROGRAMMINGMETHOD . ...................... 29 3.1 Introduction.................................29 3.2 MathematicalModel............................29 3.2.1 Dynamicprogrammingformulation................30 3.2.2 CharacterizationoftheHamiltonian...............30 3.2.3 Setoftransversalityterminalpoints................31 3.3 GeneralizedHamiltonianÂ…eld.......................32 3.3.1 Hamiltoniansystemonthestratum Z???? . .............33 3.3.2 Generalizedcharacteristic‡ow...................36 3.4 Valuefunctionandoptimaltrajectories..................37 3.5 Conclusionandcoments...........................37
Côte titre :	MAM/0724