Optimality conditions for bilevel programming problems

Focus in the article is on necessary optimality conditions for bilevel programming problems. We first identify approaches that seem to be promising. Then, two such approaches are investigated. Using the nonexistence of a descent direction for the objective function within the tangent cone to the fea...

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Bibliographic Details
Published in:Optimization Vol. 55; no. 5-6; pp. 505 - 524
Main Authors: Dempe, S., Dutta, J., Lohse, S.
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis Group 01.10.2006
Taylor & Francis LLC
Subjects:
Bilevel programming
Hierarchies
Mathematical programming
Mathematics Subject Classifications 2000: 90C46
Necessary and sufficient optimality conditions
Optimization
Studies
Vector space
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:Focus in the article is on necessary optimality conditions for bilevel programming problems. We first identify approaches that seem to be promising. Then, two such approaches are investigated. Using the nonexistence of a descent direction for the objective function within the tangent cone to the feasible set as necessary optimality condition we need efficient ways to describe this tangent cone. We describe possibilities for this in three different special cases. We conclude this article with the second approach applying Mordukhovich's coderivative to an appropriately reformulated bilevel programming problem.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331930600816189