Weakly sharp solutions and finite convergence of algorithms for a variational inequality problem

The aim of the paper is to characterize weakly sharp solutions of a variational inequality problem. In particular, we present weak sharpness results by using primal and dual gap functions, g and G, and also without considering gap functions, either. The subdifferential and locally Lipschitz properties of g + λG for λ > 0 are first studied since they are useful for discussing weakly sharp solutions of the variational inequality. A result of finite termination of a class of algorithms for solving the variational inequality problem is also studied.