Strong Stationarity for Optimal Control of Variational Inequalities of the Second Kind

Abstract

This paper is concerned with necessary optimality conditions for optimal control problems governed by variational inequalities of the second kind. So-called strong stationarity conditions are derived in an abstract framework. Strong stationarity conditions are regarded as the most rigorous ones, since they imply all other types of stationarity concepts and are equivalent to purely primal optimality conditions. The abstract framework is afterwards applied to four application-driven examples.