Global efficiency for multiobjective bilevel programming problems under generalized invexity
type: Item
instance of: scholarly article
title: Global efficiency for multiobjective bilevel programming problems under generalized invexity
zbMATH Open document ID: 1368.90140
author: Karima Bouibed
author: Hachem Slimani
author: Mohammed Said Radjef
published in: Journal of Applied Mathematics and Computing
publication date: 2017-03-07T00:00:00Z
review text: This paper deals with a nonlinear bilevel programming problem (problem NB). At the upper level, a vector optimization problem is considered while at the lower level, a scalar optimization problem arises. After giving some preliminaries and definitions, in Section 3 the KKT-conditions for the lower-level problem are used to reformulate the problem as a multi-objective single-level programming problem with equality and inequality constraints (problem MS). Sections 4 and 5 present necessary and sufficient efficiency conditions. The core of Section 4 is a Fritz John type necessary efficiency condition for problem NB. In Section 5, Fritz John type sufficient efficient conditions for a feasible point to be weakly efficient (Section 5.1), efficient (Section 5.2) and properly efficient (Section 5.3) for problem MS are given under different forms of generalized invexity and infineness. In Section 6, the case is studied where the optimization problems at both levels are linear. Two examples are discussed to illustrate the results obtained in this paper.
reviewed by: Frank Werner
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 26A51
Mathematics Subject Classification ID: 90C05
zbMATH DE Number: 6692498
zbMATH Keywords: multi-objective bilevel programming
zbMATH Keywords: KKT conditions
zbMATH Keywords: necessary and sufficient efficiency conditions
zbMATH Keywords: generalized invexity
MaRDI profile type: Publication
full work available at URL: s12190-015-0979-2
OpenAlex ID: W2287695116
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DOI: 10.1007/S12190-015-0979-2
description: scientific article; zbMATH DE number 6692498