Optimal Control of Evolution Macro-Hybrid Mixed Variational Inclusions

Abstract

Optimal control problems governed by primal and dual evolution macro-hybrid mixed variational state inclusions, in reflexive Banach spaces, are studied. This is a spatially localized macro-hybrid variational version of our mixed optimal control theory published in Appl. Math. Optim. 68, 2013, 445-473, where the solvability analysis of the state systems is given in terms of duality principles, and the mixed optimality analysis is performed via a perturbation conjugate duality method. Applications to nonlinear constrained problems from mechanics exemplify the theory.