Global efficiency for multiobjective bilevel programming problems under generalized invexity

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• 作者：Karima Bouibed ; Hachem Slimani…
• 关键词：Multiobjective bilevel programming ; KKT conditions ; Generalized invexity ; Efficiency conditions ; (Weakly ; properly) efficient solution
• 刊名：Journal of Applied Mathematics and Computing
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：53
• 期：1-2
• 页码：507-530
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theory of Computation; Mathematics of Computing;
• 出版者：Springer Berlin Heidelberg
• ISSN：1865-2085
• 卷排序：53

文摘

In this paper, we consider a nonlinear optimistic bilevel programming problem \(({\textit{NMBP}})\) 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 reformulate the bilevel programming problem into a nonlinear multiobjective single-level programming problem with equality and inequality constraints \(({\textit{MP}})\). Similarly to Dempe and Dutta (2012), we establish relationships between the problems \(({\textit{NMBP}})\) and \(({\textit{MP}})\). We prove that under appropriate constraint qualification and convexity assumptions, global (weakly or properly) efficient solutions of \(({\textit{MP}})\) correspond to global (weakly or properly) efficient solutions of \(({\textit{NMBP}})\). We establish Fritz John type necessary efficiency conditions for \(({\textit{NMBP}})\) without using any constraint qualification. Furthermore, we obtain (Fritz John type) sufficient efficiency conditions for a feasible point of \(({\textit{MP}})\) corresponds to a (weakly or properly) efficient solution for the bilevel problem \(({\textit{NMBP}})\) under various forms of generalized invexity and infineness. Moreover, a linear multiobjective bilevel programming problem is studied and sufficient efficiency conditions are derived. To illustrate the obtained results some examples are given.