Pontryagin’s principle for state-constrained evolutionary differential complementarity system

This paper is devoted to the state-constrained optimal control problem of evolutionary variational inequality. In this paper, the control domain is not necessarily convex. Moreover, since our state constraint is quite general and, in many cases, it requires pointwise behavior of the state, the framework of the partial differential equation (instead of the abstract framework) is used. Some optimality conditions (in the form of Pontryagin’s principle) for optimal controls are established.