Sensitivity Analysis and the Adjoint Update Strategy for Optimal Control Problems with Mixed Control-state Constraints

In this article, an optimal control problem subject to a semilinear elliptic equation and mixed control-state constraints is investigated. The problem data depends on certain parameters. Under an assumption of seperation of the active sets and a second-order sufficient optimality condition, Bouliganddifferentiability (B-differentiability) of the solutions with respect to the parameter is established. Furthermore, an adjoint update strategy is proposed which yields a better approximation of the optimal controls and multipliers than the classical Taylor expansion, with remainder terms vanishing in L∞.