Conjugate Duality and the Control of Linear Discrete Systems

In this paper we deal with the minimization of a convex function over the solution set of a range inclusion problem determined by a multivalued operator with convex graph. We attach a dual problem to it, provide regularity conditions guaranteeing strong duality and derive for the resulting primal-dual pair necessary and sufficient optimality conditions. We also discuss the existence of optimal solutions for the primal and dual problems by using duality arguments. The theoretical results are applied in the context of the control of linear discrete systems.