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Necessary optimality conditions for bilevel optimization problems using convexificators. (English) Zbl 1090.49021
Summary: In this work, we use a notion of convexificator [V. Jeyakumar and D. T. Luc, J. Optimization Theory Appl. 101, No. 3, 599–621 (1999; Zbl 0956.90033)] to establish necessary optimality conditions for bilevel optimization problems. For this end, we introduce an appropriate regularity condition to help us discern the Lagrange-Kuhn-Tucker multipliers.

MSC:
49J52 Nonsmooth analysis
49K99 Optimality conditions
90C25 Convex programming
90C46 Optimality conditions and duality in mathematical programming
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