Minimax control for evolutionary variational bilateral problem Original Research Article

This paper deals with a minimax control problem for semilinear evolutionary variational inequalities associated with bilateral constraints. The control domain is not necessarily convex. The cost functional, which is to be minimized, is the sup norm of some function of the state and the control. The major novelty of such a problem lies in the simultaneous presence of the nonsmooth state equation (variational inequality) and the nonsmooth cost functional (the sup norm). In this paper, the existence and the Pontryagin type necessary condition for optimal controls are established.