4 papers
Locally-averaged McCormick relaxations for discretization-regularized inverse problems
Barbara Kaltenbacher, Paul Manns
In this paper, by means of a standard model problem, we devise an approach to computing approximate dual bounds for use in global optimization of coefficient identification in part…
Minimizing and Maximizing the Shannon Entropy for Fixed Marginals
Paula Franke, Kay Hamacher, Paul Manns
The mutual information (MI) between two random variables is an important correlation measure in data analysis. The Shannon entropy of a joint probability distribution is the variab…
Convergence of trust-region algorithms in metric spaces
Paul Manns
Trust-region algorithms can be applied to very abstract optimization problems because they do not require a specific direction of descent or gradient. This has lead to recent inter…
Homotopy trust-region method for phase-field approximations in perimeter-regularized binary optimal control
Paul Manns, Vanja NikoliÄ
We consider optimal control problems that have binary-valued control input functions and a perimeter regularization. We develop and analyze a trust-region algorithm that solves a s…