Solvability of Multivalued General Mixed Variational Inequalities

In this paper, we use the auxiliary principle technique to suggest a new class of predictor-corrector algorithms for solving multivalued general mixed variational inequalities. The convergence of the proposed method only requires the partially relaxed strong monotonicity of the operator, which is weaker than co-coercivity. As special cases, we obtain a number of known and new results for solving various classes of variational inequalities.