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Necessary optimality conditions for bilevel set optimization problems

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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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Authors and Affiliations

  1. Department of Mathematics and Computers Sciences, Technical University Bergakademie Freiberg, Freiberg, Germany

    S. Dempe

  2. Department of Mathematics, Sidi Mohamed Ben Abdellah University, Dhar Al Mehrez, B.P. 1796, Atlas, Fez, Marokko

    N. Gadhi

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  1. S. Dempe
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  2. N. Gadhi
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Dempe, S., Gadhi, N. Necessary optimality conditions for bilevel set optimization problems. J Glob Optim 39, 529–542 (2007). https://doi.org/10.1007/s10898-007-9154-0

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  • DOI: https://doi.org/10.1007/s10898-007-9154-0

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