Necessary optimality conditions and a new approach to multiobjective bilevel optimization problems
type: Item
instance of: scholarly article
title: Necessary optimality conditions and a new approach to multiobjective bilevel optimization problems
zbMATH Open document ID: 1267.90130
published in: Journal of Optimization Theory and Applications
publication date: 2013-01-29T00:00:00Z
review text: A multiobjective bilevel optimization problem using the optimistic approach is investigated. It is assumed that the leader presupposes cooperation of the follower in the sense that the latter will choose in each time that solution in the solution set of his/her parametric optimization problem which is best suited with respect to the leader's objective function. Using the concept of Pareto optimality, together with a special scalarization function introduced in [\textit{J.-B. Hiriart-Urruty}, Math. Oper. Res. 4, 79--97 (1979; Zbl 0409.90086); \textit{J.-B. Hiriart-Urruty} and \textit{C. Lemaréchal}, Convex analysis and minimization algorithms. Part 1: Fundamentals. Grundlehren der Mathematischen Wissenschaften 305. Berlin: Springer-Verlag (1993; Zbl 0795.49001)], the authors give necessary optimality conditions. Several intermediate optimization problems are introduced to help in the investigation.
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C46
zbMATH DE Number: 6132211
zbMATH Keywords: multiobjective optimization
zbMATH Keywords: local weak efficient solution
zbMATH Keywords: optimality conditions
zbMATH Keywords: optimal value function
zbMATH Keywords: bilevel programming
author: Nazih Abderrazzak Gadhi
author: Stephan Dempe
reviewed by: Francisco Guerra Vazquez
MaRDI profile type: Publication
full work available at URL: s10957-012-0046-1
OpenAlex ID: W1994436307
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DOI: 10.1007/S10957-012-0046-1
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description: scientific article; zbMATH DE number 6132211