A projection subgradient method for solving optimization with variational inequality constraints

Abstract

In this paper, we propose a projection subgradient method for solving some classical variational inequality problem over the set of solutions of mixed variational inequalities. Under the conditions that \(T\) is a \(\Theta \)-pseudomonotone mapping and \(A\) is a \(\rho \)-strongly pseudomonotone mapping, we prove the convergence of the algorithm constructed by projection subgradient method. Our algorithm can be applied for instance to some mathematical programs with complementarity constraints.