A simply constrained optimization reformulation of KKT systems arising from variational inequalities

The Karush-Kuhn-Tucker (KKT) conditions can be regarded as optimality conditions for both variational inequalities and constrained optimization problems. In order to overcome some drawbacks of recently proposed reformulations of KKT systems, we propose casting KKT systems as a minimization problem with nonnegativity constraints on some of the variables. We prove that, under fairly mild assumptions, every stationary point of this constrained minimization problem is a solution of the KKT conditions. Based on this reformulation, a new algorithm for the solution of the KKT conditions is suggested and shown to have some strong global and local convergence properties.