20 citations · 52 across the 33 of their papers we have counts for
9 papers · 1 filter
Semismoothness for Solution Operators of Obstacle-Type Variational Inequalities with Applications in Optimal Control
Constantin Christof, Gerd Wachsmuth
We prove that solution operators of elliptic obstacle-type variational inequalities (or, more generally, locally Lipschitz continuous functions possessing certain pointwise-a.e. co…
Numerical Approximation of Optimal Convex and Rotationally Symmetric Shapes for an Eigenvalue Problem arising in Optimal Insulation
Hedwig Keller, Sören Bartels, Gerd Wachsmuth
We are interested in the optimization of convex domains under a PDE constraint. Due to the difficulties of approximating convex domains in , the restriction to rotati…
Second-order conditions for non-uniformly convex integrands: quadratic growth in
Daniel Wachsmuth, Gerd Wachsmuth
We study no-gap second-order optimality conditions for a non-uniformly convex and non-smooth integral functional. The integral functional is extended to the space of measures. The…
M-stationarity for a class of MPCCs in Lebesgue spaces
Felix Harder, Gerd Wachsmuth
We show that an optimality condition of M-stationarity type holds for minimizers of a class of mathematical programs with complementarity constraints (MPCCs) in Lebesgue spaces. We…
From resolvents to generalized equations and quasi-variational inequalities: existence and differentiability
Gerd Wachsmuth
We consider a generalized equation governed by a strongly monotone and Lipschitz single-valued mapping and a maximally monotone set-valued mapping in a Hilbert space. We are intere…
Maximal monotone operators with non-maximal graphical limit
Gerd Wachsmuth
We present a counterexample showing that the graphical limit of maximally monotone operators might not be maximally monotone. We also characterize the directional differentiability…
Subdifferentiation of nonconvex sparsity-promoting functionals on Lebesgue spaces
Patrick Mehlitz, Gerd Wachsmuth
Sparsity-promoting terms are incorporated into the objective functions of optimal control problems in order to ensure that optimal controls vanish on large parts of the underlying…
Lipschitz Stability and Hadamard Directional Differentiability for Elliptic and Parabolic Obstacle-Type Quasi-Variational Inequalities
Constantin Christof, Gerd Wachsmuth
This paper is concerned with the sensitivity analysis of a class of parameterized fixed-point problems that arise in the context of obstacle-type quasi-variational inequalities. We…
An Augmented Lagrangian Method for Optimization Problems with Structured Geometric Constraints
Xiaoxi Jia, Christian Kanzow, Patrick Mehlitz +1
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifi…