Application of penalty methods to generalized variational inequalities in Banach spaces

In this paper, we consider a class of generalized variational inequalities (GVI) in infinite dimensional Banach spaces, in which only approximation sequences for GVI are known instead of exact values of the cost mapping and feasible set. A sequence of inexact solutions of auxiliary problems involving general penalty method is introduced. We obtain some convergence properties of the perturbed version of the regularized penalty method under mild coercive conditions, which extend some well-known results of variational inequalities in many respects.