Second-Order Optimality Conditions for Boundary Control Problems with Mixed Pointwise Constraints

Abstract

This paper deals with second-order optimality conditions for a boundary control problem which is governed by semilinear elliptic equations with mixed pointwise state-control constraints. We show that in some cases, there is no gap between second-order necessary optimality conditions and second-order sufficient optimality conditions. In addition, second-order sufficient optimality conditions for the problem where the objective function does not depend on control variables are also discussed.