New inertial proximal algorithms for solving multivalued variational inequalities

This paper presents two new algorithms for solving multivalued variational inequality problems in a real Hilbert space.By combining the nonexpansiveness of proximal operators associated with the proper lower semicontinuous convex function of the problems and inertial techniques, we demonstrate the weak convergence of the iteration sequences generated by our first algorithm under monotone and Lipschitz continuous assumptions of the cost mappings.Next, we use Mann iteration technique to obtain the second algorithm and show its strong convergence.Finally, we give some numerical results for two proposed algorithms and comparison with some other known algorithms.