Characterization of weakly sharp solutions of a variational inequality by its primal gap function

摘要

Our aim is to study weakly sharp solutions of a variational inequality in terms of its primal gap function g. We discuss sufficient conditions for the Lipschitz continuity and subdifferentiability of the primal gap function. Several sufficient conditions for the relevant mapping to be constant on the solutions have also been obtained. Based on these, we characterize the weak sharpness of the solutions of a variational inequality by g. Some finite convergence results of algorithms for solving variational inequality problems are also included.