The generalized set-valued strongly nonlinear implicit variational inequalities

In this paper, we introduce and study a new class of generalized set-valued strongly nonlinear implicit variational inequalities in Hilbert spaces. We construct the algorithm for solving this kind of generalized set-valued strongly nonlinear implicit variational inequality problem by using the auxiliary principle technique of Glowinski, Lions, and Tremolieres, prove the existence of solutions for this class of generalized set-valued strongly nonlinear implicit variational inequalities and the convergence of iterative sequences generated by the algorithm.