20 citations · 52 across the 33 of their papers we have counts for
38 papers
Energy Space Newton Differentiability for Solution Maps of Unilateral and Bilateral Obstacle Problems
Constantin Christof, Gerd Wachsmuth
We prove that the solution operator of the classical unilateral obstacle problem on a nonempty open bounded set , , is Newton differentiabl…
Stability and genericity of bang-bang controls in affine problems
Alberto Domínguez Corella, Gerd Wachsmuth
We analyse the role of the bang-bang property in affine optimal control problems. We show that many essential stability properties of affine problems are only satisfied when minimi…
Bilevel Optimal Control: Theory, Algorithms, and Applications
Stephan Dempe, Markus Friedemann, Felix Harder +2
In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given meas…
Variational Poisson Denoising via Augmented Lagrangian Methods
Christian Kanzow, Fabius Krämer, Patrick Mehlitz +2
In this paper, we denoise a given noisy image by minimizing a smoothness promoting function over a set of local similarity measures which compare the mean of the given image and so…
Slater conditions without interior points for programs in Lebesgue spaces with pointwise bounds and finitely many constraints
Gerd Wachsmuth
We consider optimization problems in Lebesgue spaces with pointwise box constraints and finitely many additional linear constraints. We prove that the existence of a Slater point w…
Non-existence of perturbed solutions under a second-order sufficient condition
Gerd Wachsmuth
We present an optimization problem in infinite dimensions which satisfies the usual second-order sufficient condition but for which perturbed problems fail to possess solutions.
Integer optimal control problems with total variation regularization: Optimality conditions and fast solution of subproblems
Jonas Marko, Gerd Wachsmuth
We investigate local optimality conditions of first and second order for integer optimal control problems with total variation regularization via a finite-dimensional switching poi…
A simple proof of the Baillon-Haddad theorem on open subsets of Hilbert spaces
Daniel Wachsmuth, Gerd Wachsmuth
We give a simple proof of the Baillon-Haddad theorem for convex functions defined on open and convex subsets of Hilbert spaces. We also state some generalizations and limitations.…
Finding global solutions of some inverse optimal control problems using penalization and semismooth Newton methods
Markus Friedemann, Felix Harder, Gerd Wachsmuth
We present a method to solve a special class of parameter identification problems for an elliptic optimal control problem to global optimality. The bilevel problem is reformulated…
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…
First-order conditions for the optimal control of the obstacle problem with state constraints
Ira Neitzel, Gerd Wachsmuth
We consider an optimal control problem in which the state is governed by an unilateral obstacle problem (with obstacle from below) and restricted by a pointwise state constraint (f…
Non-optimality of conical parts for Newton's problem of minimal resistance in the class of convex bodies and the limiting case of infinite height
Lev Lokutsievskiy, Gerd Wachsmuth, Mikhail Zelikin
We consider Newton's problem of minimal resistance, in particular we address the problem arising in the limit if the height goes to infinity. We establish existence of solutions an…
Reformulation of the M-stationarity conditions as a system of discontinuous equations and its solution by a semismooth Newton method
Felix Harder, Patrick Mehlitz, Gerd Wachsmuth
We show that the Mordukhovich-stationarity system associated with a mathematical program with complementarity constraints (MPCC) can be equivalently written as a system of disconti…
New Constraint Qualifications for Optimization Problems in Banach Spaces based on Asymptotic KKT Conditions
Eike Börgens, Christian Kanzow, Patrick Mehlitz +1
Optimization theory in Banach spaces suffers from the lack of available constraint qualifications. Despite the fact that there exist only a very few constraint qualifications, they…
Elliptic quasi-variational inequalities under a smallness assumption: Uniqueness, differential stability and optimal control
Gerd Wachsmuth
We consider a quasi-variational inequality governed by a moving set. We employ the assumption that the movement of the set has a small Lipschitz constant. Under this requirement, w…
On Second-Order Optimality Conditions for Optimal Control Problems Governed by the Obstacle Problem
Constantin Christof, Gerd Wachsmuth
This paper is concerned with second-order optimality conditions for Tikhonov regularized optimal control problems governed by the obstacle problem. Using a simple observation that…