FIRST-ORDER METHODS FOR GENERALIZED OPTIMAL CONTROL PROBLEMS FOR SYSTEMS WITH DISTRIBUTED PARAMETERS

The problems of optimization of linear distributed systems with generalized control and first-order methods for their solution are considered. The main focus is on proving the convergence of methods. It is assumed that the operator describing the model satisfies a priori estimates in negative norms. For control problems with convex and preconvex admissible sets, the convergence of several first-order algorithms with errors in iterative subproblems is proved.