On Optimization Problems with Variational Inequality Constraints

Abstract

This paper is devoted to a class of optimization problems that contain variational inequality or nonlinear complementarity constraints. Problems of this kind arise, for example, in game theory, bilevel programming, and the design of networks subject to equilibrium conditions. For such problems first-order necessary optimality conditions are derived and a numerical approach is proposed, based on nondifferentiable optimization techniques. This approach is illustrated by simple examples.