76 citations · 106 across the 15 of their papers we have counts for
18 papers
No-gap second-order conditions for optimization problems involving transport distances
Nicolas Borchard, Christian Meyer, Gerd Wachsmuth
We consider optimization problems in the space of measures. As a regularization term, the problem includes the transport distance to a given prior measure. For the derivation of se…
On a Lack of Stability of Parametrized BV Solutions to Rate-Independent Systems with Non-Convex Energies and Discontinuous Loads
Merlin Andreia, Christian Meyer
We consider a rate-independent system with nonconvex energy under discontinuous external loading. The underlying space is finite dimensional and the loads are functions in $BV([0,T…
Finite Element Approximation of Data-Driven Problems in Conductivity
Christian Meyer, Annika Müller
This paper is concerned with the finite element discretization of the data driven approach according to arXiv:1510.04232 for the solution of PDEs with a material law arising from m…
Bilevel Optimization of the Kantorovich Problem and its Quadratic Regularization Part II: Convergence Analysis
Sebastian Hillbrecht, Paul Manns, Christian Meyer
This paper is concerned with an optimization problem that is constrained by the Kantorovich optimal transportation problem. This bilevel optimization problem can be reformulated as…
An Adaptive Time Stepping Scheme for Rate-Independent Systems with Non-Convex Energy
Merlin Andreia, Christian Meyer
We investigate a local incremental stationary scheme for the numerical solution of rate-independent systems. Such systems are characterized by a (possibly) non-convex energy and a…
Parabolic optimal control problems with combinatorial switching constraints -- Part II: Outer approximation algorithm
Christoph Buchheim, Alexandra Grütering, Christian Meyer
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switc…
Parabolic optimal control problems with combinatorial switching constraints -- Part I: Convex relaxations
Christoph Buchheim, Alexandra Grütering, Christian Meyer
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switc…
-Regularization of the Beckmann Problem
Dirk Lorenz, Hinrich Mahler, Christian Meyer
We investigate the problem of optimal transport in the so-called Beckmann form, i.e. given two Radon measures on a compact set, we seek an optimal flow field which is a vector valu…
A Priori Error Analysis for an Optimal Control Problem Governed by a Variational Inequality of the Second Kind
Christian Meyer, Monika Weymuth
We consider an optimal control problem governed by an elliptic variational inequality of the second kind. The problem is discretized by linear finite elements for the state and a v…
Optimal Control of Perfect Plasticity Part II: Displacement Tracking
Christian Meyer, Stephan Walther
The paper is concerned with an optimal control problem governed by the rate-independent system of quasi-static perfect elasto-plasticity. The objective is optimize the displacement…
Optimal Control of Perfect Plasticity Part I: Stress Tracking
Christian Meyer, Stephan Walther
The paper is concerned with an optimal control problem governed by the rate-independent system of quasi-static perfect elasto-plasticity. The objective is to optimize the stress fi…
Optimal control of an abstract evolution variational inequality with application to homogenized plasticity
Hannes Meinlschmidt, Christian Meyer, Stephan Walther
The paper is concerned with an optimal control problem governed by a state equation in form of a generalized abstract operator differential equation involving a maximal monotone op…
A-priori error analysis of local incremental minimization schemes for rate-independent evolutions
Christian Meyer, Michael Sievers
This paper is concerned with a priori error estimates for the local incremental minimization scheme, which is an implicit time discretization method for the approximation of rate-i…
Quadratically regularized optimal transport
Dirk A. Lorenz, Paul Manns, Christian Meyer
We investigate the problem of optimal transport in the so-called Kantorovich form, i.e. given two Radon measures on two compact sets, we seek an optimal transport plan which is ano…
A non-smooth trust-region method for locally Lipschitz functions with application to optimization problems constrained by variational inequalities
Constantin Christof, Juan Carlos De Los Reyes, Christian Meyer
We propose a nonsmooth trust-region method for solving optimization problems with locally Lipschitz continuous functions, with application to problems constrained by variational in…
Optimal control of a non-smooth semilinear elliptic equation
Constantin Christof, Christian Clason, Christian Meyer +1
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 differenti…
Optimal Control of the Thermistor Problem in Three Spatial Dimensions
Hannes Meinlschmidt, Christian Meyer, Joachim Rehberg
This paper is concerned with the state-constrained optimal control of the three-dimensional thermistor problem, a fully quasilinear coupled system of a parabolic and elliptic PDE w…
Optimal Control of the Inhomogeneous Relativistic Maxwell Newton Lorentz Equations
C. Meyer, S. M. Schnepp, O. Thoma
This note is concerned with an optimal control problem governed by the relativistic Maxwell-Newton-Lorentz equations, which describes the motion of charges particles in electro-mag…