This paper provides necessary conditions of optimality for optimal control problems, in which
the pathwise constraints comprise both ‘pure’ constraints on the state variable and also ‘mixed’
constraints on control and state variables. The proofs are along the lines of earlier analysis for
mixed constraint problems, according to which Clarke’s theory of ‘stratified’ necessary conditions is
applied to a modified optimal control problem resulting from absorbing the mixed constraint into the
dynamics; the difference here is that necessary conditions which now take account of the presence
of pure state constraints are applied to the modified problem. Necessary conditions are given for a
rather general formulation of the problem containing both forms of the constraints, and then these
are specialized to apply to problems having special structure. While combined pure state and mixed
control/state problems have been previously treated in the literature, the necessary conditions in this
paper are proved under less restrictive hypotheses and for novel formulations of the constraints.