7 papers · 1 filter
Enclosing minima in nonsmooth optimization via trust regions of higher-order cutting-plane models
Bennet Gebken, Michael Ulbrich
We propose a globally convergent trust-region bundle method for minimizing lower- functions using higher-order cutting-plane models. Under certain growth assumptions on the ob…
Superlinear convergence in nonsmooth optimization via higher-order cutting-plane models
Bennet Gebken, Michael Ulbrich
A cutting-plane model for a nonsmooth function is the maximum of several first-order expansions centered at different points. Using such a model in a bundle method leads to linear…
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…
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…