A projection subgradient method for solving optimization with variational inequality constraints

摘要

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 Θ-pseudomonotone mapping and A is a ρ-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.