Monotone extensions into compact target sets in dual systems

Abstract

We study monotone extension problems in the general framework of dual systems, without assuming separation. The paper develops a compact target-set formulation that includes multivalued operators as a special case and allows the initial set to be nonmonotone. Using tools from nonlinear and convex analysis, we establish existence results and necessary and sufficient conditions for monotone extensions. Applications to variational inequalities are also obtained.