Necessary Optimality Conditions for Bilevel Optimization Problems Using Convexificators

In this work, we use a notion of convexificator (Jeyakumar, V. and Luc, D.T. (1999), Journal of Optimization Theory and Applicatons, 101, 599–621.) 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.

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