  In this paper we study an optimal control problem with nonsmooth mixed state
and control constraints. In most of the existing results, the necessary
optimality condition for optimal control problems with mixed state and control
constraints are derived under the Mangasarian-Fromovitz condition and under the
assumption that the state and control constraint functions are smooth. In this
paper we derive necessary optimality conditions for problems with nonsmooth
mixed state and control constraints under constraint qualifications based on
pseudo-Lipschitz continuity and calmness of certain set-valued maps. The
necessary conditions are stratified, in the sense that they are asserted on
precisely the domain upon which the hypotheses (and the optimality) are assumed
to hold. Moreover necessary optimality conditions with an Euler inclusion
taking an explicit multiplier form are derived for certain cases.
