Necessary optimality conditions for bilevel set optimization problems

Necessary optimality conditions for bilevel set optimization problems

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Article ID: iaor20084694
Country: Netherlands
Volume: 39
Issue: 4
Start Page Number: 529
End Page Number: 542
Publication Date: Dec 2007
Journal: Journal of Global Optimization
Authors: ,
Keywords: programming (bilevel)
Abstract:

Bilevel programming problems are hierarchical optimization problems where in the upper level problem a function is minimized subject to the graph of the solution set mapping of the lower level problem. In this paper necessary optimality conditions for such problems are derived using the notion of a convexificator by Luc and Jeyakumar. Convexificators are subsets of many other generalized derivatives. Hence, our optimality conditions are stronger than those using e.g., the generalized derivative due to Clarke or Michel-Penot. Using a certain regularity condition Karush–Kuhn–Tucker conditions are obtained.

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