Necessary optimality conditions for bilevel set optimization problems

被引：0
|
作者：
S. Dempe
N. Gadhi
机构：
[1] Technical University Bergakademie Freiberg,Department of Mathematics and Computers Sciences
[2] Sidi Mohamed Ben Abdellah University,Department of Mathematics
来源：
Journal of Global Optimization | 2007年 / 39卷
关键词：
Bilevel optimization; Convexificator; Karush-Kuhn-Tucker multipliers; Necessary Optimality conditions; Regularity condition; Set valued mappings; Support function; Primary 49J52; 90C29; Secondary 49K99;
D O I：
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学科分类号：
摘要：
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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页码：529 / 542
页数：13
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