WELL-POSEDNESS FOR VARIATIONAL INEQUALITY PROBLEMS WITH GENERALIZED MONOTONE SET-VALUED MAPS

摘要

In this paper, we introduce two new classes of generalized monotone set-valued maps, namely relaxed μ-p monotone and relaxed μ-p pseudomonotone. Relations of these classes with some other well-known classes of generalized monotone maps are investigated. Employing these new notions, we derive existence and well-posedness results for a set-valued variational inequality problem. Our results generalize some of the well-known results. A gap function is proposed for the variational inequality problem and a lower error bound is obtained under the assumption of relaxed μ-p pseudomonotonicity. An equivalence relation between the well-posedness of the variational inequality problem and that of a related optimization problem pertaining to the gap function is also presented.