Necessary conditions of optimality in the form of
Unmaximized Inclusions (UI) are derived for optimal control
problems with state constraints. The conditions presented here
generalize earlier optimality conditions to problems that may be
nonconvex.
The derivation of UI-type conditions in the absence of the convexity assumption is of particular
importance when deriving necessary conditions for constrained
problems. We illustrate this feature by establishing, as an
application, optimality conditions for problems that in addition
to state constraints incorporate mixed state-control constraints.