On numerical solution of optimal control problems with nonsmooth objectives: Application to economic models

Optimal control problems with nonsmooth objectives appear frequently in many practical situations, see e.g. [2] or [9]. For such problems the necessary optimality conditions in form of an appropriate maximum principle have been derived by Clarice [1], allowing even the system dynamics to be nonsmooth. Sufficient optimality conditions for a certain class of such problems can be found in [4]. Existing numerical methods enable us to solve problems of this kind numerically; however, we face a lot of technical difficulties in this context. In this paper we study one of these obstacles in connection with so called bundle methods, cf. [13]. It contains a generalization of the results from [9], where also the same problem has been attacked. We consider the following general model: