Département de Mathématiques

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Browsing Département de Mathématiques by Author "Bouibed, Karima"

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    Etude des concepts de solution dans les problèmes bi-niveaux multi-objectifs
    (Universite Mouloud MAMMERI Tizi-Ouzou, 2016) Bouibed, Karima
    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.