3 papers
math.OC2026
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…
math.FA2025
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…
math.OC2025
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…