  We derive a variant of the nonsmooth maximum principle for problems with pure
state constraints. The interest of our result resides on the nonsmoothness
itself since, when applied to smooth problems, it coincides with known results.
Remarkably, in the normal form, our result has the special feature of being a
sufficient optimality condition for linearconvex problems, a feature that the
classical Pontryagin maximum principle had whereas the nonsmooth version had
not. This work is distinct to previous work in the literature since, for state
constrained problems, we add the Weierstrass conditions to adjoint inclusions
using the joint subdifferentials with respect to the state and the control. Our
proofs use old techniques developed in [16], while appealing to new results in
[7].

Optimization and Control