Weak sharpness for solutions of nonsmooth variational inequalities and applications

In this paper, we first give some new characterizations of weak sharpness of the solution set of nonsmooth variational inequalities in terms of partial subdiferentials/Gâteaux derivatives of involving bifunctions. As applications, we use a new characterization to establish sufficient conditions for guaranteeing finite termination of an arbitrary algorithm solving nonsmooth variational inequalities under the weak sharpness assumption.