Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints

Abstract

In this paper we study optimization problems with variational inequality constraints in finite dimensional spaces. Kuhn-Tucker type necessary optimality conditions involving coderivatives are given under certain constraint qualifications including one that ensures nonexistence of non-trivial abnormal multipliers. The result is applied to bilevel programming problems to obtain Kuhn-Tucker type necessary optimality conditions. The Kuhn-Tucker type necessary optimality conditions are shown to be satisfied without any constraint qualification by the class of bilevel programming problems where the lower level is a parametric linear quadratic problem.