The Karush–Kuhn–Tucker (KKT) conditions can be regarded as optimality conditions for both variational inequalities and constrained optimizationproblems. In order to overcome some drawbacks of recently proposed reformulations of KKT systems, we propose casting KKT systems as a minimization problemwith nonnegativity constraints on some of the variables. We prove that, under fairlymild assumptions, every stationary point of this constrained minimization problemis a solution of the KKT conditions. Based on this reformulation, a new algorithmfor the solution of the KKT conditions is suggested and shown to have some strongglobal and local convergence properties.