COUPLING THE LQ REGULARIZATION METHOD AND THE OUTER APPROXIMATION METHOD FOR SOLVING PSEUDOMONOTONE VARIATIONAL INEQUALITIES

Abstract

In our recent papers [2, 3] we have proposed a modified logarithmicquadratic method for solving monotone generalized variational inequalities and quasimonotone multivalued variational inequalities on polyhedral. The method is based on the special logarithmic quadratic function which replaces the usual quadratic. In this paper we combine this result with the outer approximation method to obtain a new interior approximation algorithm for solving pseudomonone variational inequalities satisfying a certain Lipschitz condition on a closed convex set. Next, to avoid the Lipschitz condition we combine this technique with linesearch technique to obtain a convergent algorithm for pseudomonone variational inequalities.