A Filled Function Method for Solving Variational Inequality Problems

In this paper a filled function method is suggested for solving finite dimensional variational inequality problems over sets defined by systems of equalities and inequalities. Firstly, based on the Karush-Kuhn-Tucker (KKT) conditions of the variational inequality problems, the original problem is converted into a corresponding constrained optimization problem. Subsequently, a new filled function with one parameter is proposed for solving the constrained optimization problem. Some properties of the filled function are studied and discussed. Finally, an algorithm based on the proposed filled function for solving variational inequality problems is presented. The implementation of the algorithm on several test problems is reported with numerical results.