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

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