On sharp necessary optimality conditions in control of contact problems with strings

The paper deals with necessary optimality conditions in a special infinite-dimensional mathematical program with equilibrium constraints having a mechanical interpretation. The main hurdle consists in the computation of the limiting normal cone to the graph of the normal-cone mapping ND(⋅)ND(⋅), where DD is the cone of nonnegative functions in the Sobolev space considered. We discuss also the influence of state and mixed control–state constraints.