Necessary optimality conditions for optimal control problems with set-valued constraints

In this paper, we consider optimal control problems with set-valued state and control constraints. The present constraints subsume the existing mixed equality and inequality constraints. The necessary optimality conditions for weak local minimum are derived for these problems under calmness and constraint qualification condition on the set-valued constraints, but without any convexity or differentiability assumptions on the original data. The novelty of this paper concerns both the nature of calmness and constraint qualification condition and the analytic techniques used to derive the results.