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 logarithmic

quadratic method for solving monotone generalized variational inequal

ities and quasimonotone multivalued variational inequalities on polyhe

dral. The method is based on the special logarithmic quadratic function

which replaces the usual quadratic. In this paper we combine this re

sult with the outer approximation method to obtain a new interior ap

proximation 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