Optimal control problems with nonsmooth mixed constraints

In this paper we present a weak maximum principle for optimal control problems involving mixed constraints and pointwise set control constraints. Notably such result holds for problems with possibly nonsmooth mixed constraints. Although the setback of such result resides on a convexity assumption on the ¿extended velocity set¿, we show that if the number of mixed constraints is one, such convexity assumption may be removed when an interiority assumption holds.