This paper is concerned with an optimal control problem governed by a non-smooth
semilinear elliptic equation. We show that the control-to-state mapping is directionally …

We consider the distributed optimal control of the obstacle problem with control constraints.
Since Mignot proved in 1976 the necessity of a system which is equivalent to strong …

This paper is concerned with an optimal control problem governed by a semilinear,
nonsmooth operator differential equation. The nonlinearity is locally Lipschitz-continuous …

Comparison of optimality systems for the optimal control of the obstacle problem Page 1
GAMM-Mitt. 40, No. 4, 312 – 338 (2017) / DOI 10.1002/gamm.201740004 Comparison of …

We consider an optimal control problem, whose state is given as the solution of the obstacle
problem. The controls are not assumed to be dense in H^-1(Ω). Hence, local minimizers may …

We consider an optimal control problem of tracking type governed by a time-discrete
regularized phase-field fracture or damage propagation model. The energy minimization …

In general, standard necessary optimality conditions cannot be formulated in a
straightforward manner for semismooth shape optimization problems. In this paper, we …

We investigate optimality conditions for optimization problems constrained by a class of
variational inequalities of the second kind. Based on a nonsmooth primal–dual reformulation …

Within this chapter, we discuss control in the coefficients of an obstacle problem. Utilizing
tools from H-convergence, we show existence of optimal solutions. First order necessary …

This article is concerned with the derivation of a posteriori error estimates for optimization
problems subject to an obstacle problem. To circumvent the nondifferentiability inherent to …