6 papers
On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation
Katharina Bieker, Bennet Gebken, Sebastian Peitz
We present a novel algorithm that allows us to gain detailed insight into the effects of sparsity in linear and nonlinear optimization, which is of great importance in many scienti…
An efficient descent method for locally Lipschitz multiobjective optimization problems
Bennet Gebken, Sebastian Peitz
In this article, we present an efficient descent method for locally Lipschitz continuous multiobjective optimization problems (MOPs). The method is realized by combining a theoreti…
ROM-based multiobjective optimization of elliptic PDEs via numerical continuation
Stefan Banholzer, Bennet Gebken, Michael Dellnitz +2
Multiobjective optimization plays an increasingly important role in modern applications, where several objectives are often of equal importance. The task in multiobjective optimiza…
On the Equivariance Properties of Self-adjoint Matrices
Michael Dellnitz, Bennet Gebken, Raphael Gerlach +1
We investigate self-adjoint matrices with respect to their equivariance properties. We show in particular that a matrix is self-adjoint if and only if it is…
Inverse multiobjective optimization: Inferring decision criteria from data
Bennet Gebken, Sebastian Peitz
It is a very challenging task to identify the objectives on which a certain decision was based, in particular if several, potentially conflicting criteria are equally important and…
On the hierarchical structure of Pareto critical sets
Bennet Gebken, Sebastian Peitz, Michael Dellnitz
In this article we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems…