Some aspects of nonsmooth variational inequalities on Hadamard manifolds

This is the first paper dealing with the study of minimum and maximum principle sufficiency properties for nonsmooth variational inequalities by using gap functions in the setting of Hadamard manifolds. We also provide some characterizations of these two sufficiency properties. We conclude the paper with a discussion of the error bounds for nonsmooth variational inequalities in the setting of Hadamard manifolds.

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 nonsmoothvariational inequalities in terms of partial subdiferentials/Gˆateaux derivatives of involving bifunctions. Asapplications, we use a new characterization to establish sufficient conditions for guaranteeing finite terminationof an arbitrary algorithm solving nonsmooth variational inequalities under the weak sharpness assumption