CONVERGENCE OF STATIONARY-SEQUENCES FOR VARIATIONAL-INEQUALITIES WITH MAXIMAL MONOTONE-OPERATORS

Let T be a maximal monotone operator defined on R(N). In this paper we consider the associated variational inequality 0 is-an-element-of T(x*) and stationary sequences {x(k)*} for this operator, i.e., satisfying T(x(k)*) --> 0. The aim of this paper is to give sufficient conditions ensuring that these sequences converge to the solution set T - 1(0) especially when they are unbounded. For this we generalize and improve the directionally local boundedness theorem of Rockafellar to maximal monotone operators T defined on R(N).