1 citations · 1 across the 6 of their papers we have counts for
8 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…
A trust-region method for optimal control of ODEs with continuous-or-off controls and TV regularization
Markus Friedemann, Gerd Wachsmuth
A solution algorithm for a special class of optimal control problems subject to an ordinary differential equation is proposed. The controls possess a continuous-or-off structure an…
Characterization of Hilbertizable spaces via convex functions
Nicolas Borchard, Gerd Wachsmuth
We show that the existence of a strongly convex function with a Lipschitz derivative on a Banach space already implies that the space is isomorphic to a Hilbert space. Similarly, i…
Numerical solution of optimal control problems using quadratic transport regularization
Nicolas Borchard, Gerd Wachsmuth
We address optimal control problems on the space of measures for an objective containing a smooth functional and an optimal transport regularization. That is, the quadratic Monge-K…
Subdifferentials and penalty approximations of the obstacle problem
Amal Alphonse, Gerd Wachsmuth
We consider a framework for approximating the obstacle problem through a penalty approach by nonlinear PDEs. By using tools from capacity theory, we show that derivatives of the so…
Vector-Valued Integer Optimal Control with TV Regularization: Optimality Conditions and Algorithmic Treatment
Jonas Marko, Gerd Wachsmuth
We investigate a broad class of integer optimal control problems with vector-valued controls and switching regularization using a total variation functional involving the p-norm, w…
Minimal and maximal solution maps of elliptic QVIs of obstacle type: Lipschitz stability, differentiability and optimal control
Amal Alphonse, Michael Hintermüller, Carlos N. Rautenberg +1
Quasi-variational inequalities (QVIs) of obstacle type in many cases have multiple solutions that can be ordered. We study a multitude of properties of the operator mapping the sou…
Second-order conditions for spatio-temporally sparse optimal control via second subderivatives
Nicolas Borchard, Gerd Wachsmuth
We address second-order optimality conditions for optimal control problems involving sparsity functionals which induce spatio-temporal sparsity patterns. We employ the notion of (w…