Necessary optimality conditions for bilevel set optimization problems |
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| Authors: | S Dempe N Gadhi |
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| Institution: | (1) Department of Mathematics and Computers Sciences, Technical University Bergakademie Freiberg, Freiberg, Germany;(2) Department of Mathematics, Sidi Mohamed Ben Abdellah University, Dhar Al Mehrez, B.P. 1796, Atlas, Fez, Marokko |
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| 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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| Keywords: | Bilevel optimization Convexificator Karush-Kuhn-Tucker multipliers Necessary Optimality conditions Regularity condition Set valued mappings Support function |
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