Weak sharpness and finite convergence for mixed variational inequalities

Weak sharp solutions of mixed variational inequalities are introduce and studied in Hilbert spaces. Several characterizations of weak sharpness of solutions of mixed variational inequalities without using gap functions are given. It is proved that sequences generated by an inexact proximal point algorithm terminate after a finite number of iterations for solutions of mixed variational inequalities provided that their solution sets are weakly sharp. Examples are also given to illustrate our results.