THE ADJOINT ARC IN NONSMOOTH OPTIMIZATION

We extend the theory of necessary conditions for nonsmooth problems of Bolza in three ways: first, we incorporate state constraints of the intrinsic type x(t) is-an-element-of X(t) for all t; second, we make no assumption of calmness or normality; and third, we show that a single adjoint function of bounded variation simultaneously satisfies the Hamiltonian inclusion, the Euler-Lagrange inclusion, and the Weierstrass-Pontryagin maximum condition, along with the usual transversality relations.