The Adjoint Arc in Nonsmooth Optimization

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Abstract
We extend the theory of necessary conditions for nonsmooth problems of Bolza in three ways: first, we incorporate state constraints of the intrinsic type $x(t) \in X(t)$ 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.

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