NECESSARY OPTIMALITY CONDITIONS FOR OPTIMIZATION PROBLEMS WITH VARIATIONAL INEQUALITY CONSTRAINTS

In this paper we study optimization problems with variational inequali ty constraints in mine finite dimensional spaces. Kuhn-Tucker type nec essary optimality conditions involving coderivatives are given under c ertain constraint qualifications including one that ensures nonexisten ce of nontrivial abnormal multipliers. The result is applied to bileve l 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 clas s of bilevel programming problems where the lower level is a parametri c linear quadratic problem.