26 citations · 35 across the 15 of their papers we have counts for
7 papers · 1 filter
Mean-field optimal control for biological pattern formation
Martin Burger, Lisa Maria Kreusser, Claudia Totzeck
We propose a mean-field optimal control problem for the parameter identification of a given pattern. The cost functional is based on the Wasserstein distance between the probabilit…
An entropic Landweber method for linear ill-posed problems
Martin Burger, Elena Resmerita, Martin Benning
The aim of this paper is to investigate the use of an entropic projection method for the iterative regularization of linear ill-posed problems. We derive a closed form solution for…
Data assimilation in price formation
Martin Burger, Jan-Frederik Pietschmann, Marie-Therese Wolfram
We consider the problem of estimating the density of buyers and vendors in a nonlinear parabolic price formation model using measurements of the price and the transaction rate. Our…
Mean-field optimal control and optimality conditions in the space of probability measures
Martin Burger, René Pinnau, Claudia Totzeck +1
We derive a framework to compute optimal controls for problems with states in the space of probability measures. Since many optimal control problems constrained by a system of ordi…
Solution Paths of Variational Regularization Methods for Inverse Problems
Leon Bungert, Martin Burger
We consider a family of variational regularization functionals for a generic inverse problem, where the data fidelity and regularization term are given by powers of a Hilbert norm…
Bregman Distances in Inverse Problems and Partial Differential Equation
Martin Burger
The aim of this paper is to provide an overview of recent development related to Bregman distances outside its native areas of optimization and statistics. We discuss approaches in…