Etude des concepts de solution dans les problèmes bi-niveaux multi-objectifs
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Date
2016
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Universite Mouloud MAMMERI Tizi-Ouzou
Abstract
In this thesis, we have studied the sufficient efficiency conditions in multi-objective
bi-level programming problems. For this, we have firstly considered a nonlinear optimistic
bi-level programming problem (PBMN), where the upper level is a vector
optimization problem and the lower level is a scalar optimization problem. By using
the Karush–Kuhn–Tucker conditions associated to the lower-level problem, we have
transformed the problem (PBMN) into a nonlinear multiobjective single-level programming
problem with equality and inequality constraints (PMN). We have established
relationships between the problems (PBMN) and (PMN), and in particular
we have shown under appropriate constraint qualification and convexity assumptions
that the sets of global (weakly or properly) efficient solutions of problems (PBMN)
and (PMN) coincide. Furthermore, we have proved Fritz John type necessary efficiency
conditions for (PBMN) without using any constraint qualification. Moreover,
we have obtained (Fritz John) type sufficient efficiency conditions for a feasible point
of (PMN) corresponds to a (weakly or properly) efficient solution for the bilevel
problem (PBMN) under various forms of generalized invexity and infineness. On
the other hand, we have generalized the above results by considering other multiobjective
bi-level problems involving linear, quadratic, and/or fractional functions.
To illustrate the obtained results several examples are given.
Keywords : Multiobjective bilevel programming, Fractional programming, KKT
conditions, Generalized invexity, Global efficiency conditions, (Weakly, properly) efficient
solution.
Description
Karima Bouibed, Dir. Mohammed Said Radjef. - [s.l] : [s.n], 2016. - 104 f. ; 30cm. + CD rom.
Keywords
Problème multi-objectif, Problème bi-niveau
Citation
RECHERCHE OPERATIONNELLE ET OPTIMISATION