5 papers · 1 filter
On Discrete Subproblems in Integer Optimal Control with Total Variation Regularization in Two Dimensions
Paul Manns, Marvin Severitt
We analyze integer linear programs which we obtain after discretizing two-dimensional subproblems arising from a trust-region algorithm for mixed integer optimal control problems w…
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…
A simplified Newton method to generate snapshots for POD models of semilinear optimal control problems
Paul Manns, Stefan Ulbrich
In PDE-constrained optimization, proper orthogonal decomposition (POD) provides a surrogate model of a (potentially expensive) PDE discretization, on which optimization iterations…
Relaxed multibang regularization for the combinatorial integral approximation
Paul Manns
Multibang regularization and combinatorial integral approximation decompositions are two actively researched techniques for integer optimal control. We consider a class of polyhedr…
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…