A-posteriori verification of optimality conditions for control problems with finite-dimensional control space

In this paper we investigate non-convex optimal control problems. We are concerned with a-posteriori verification of sufficient optimality conditions. If the proposed verification method confirms the fulfillment of the sufficient condition then a-posteriori error estimates can be computed. A special ingredient of our method is an error analysis for the Hessian of the underlying optimization problem. We derive conditions under which positive definiteness of the Hessian of the discrete problem implies positive definiteness of the Hessian of the continuous problem. The article is complemented with numerical experiments.