Convex Functional Control Problems for Nonlinear Evolution Equations Governed by Time-Dependent Subdifferentials

We establish the abstract theory of convex functional control problems for nonlinear evolution equations governed by time-dependent subdifferentials. Namely, we prove the existence of an optimal convex functional control that minimizes the nonlinear cost functional. Moreover, we consider the generalization of optimal convex functional control problems by using the concept of the local gap of two control convex functions. Furthermore, we consider singular optimal functional control problems for quasivariational state systems. Finally, we apply our general result to some model problems.