26 citations · 88 across the 16 of their papers we have counts for
16 papers
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…
Technical results on the convergence of quasi-Newton methods for nonsmooth optimization
Bennet Gebken
It is well-known by now that the BFGS method is an effective method for minimizing nonsmooth functions. However, despite its popularity, theoretical convergence results are almost…
Analyzing the speed of convergence in nonsmooth optimization via the Goldstein subdifferential with application to descent methods
Bennet Gebken
The Goldstein -subdifferential is a relaxed version of the Clarke subdifferential which has recently appeared in several algorithms for nonsmooth optimization. With it…
A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces
Konstantin Sonntag, Bennet Gebken, Georg Müller +2
The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from [1] is extended from finite-dimensional problems to general Hilbert spa…
A note on the convergence of deterministic gradient sampling in nonsmooth optimization
Bennet Gebken
Approximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for…
Multiobjective Optimization of Non-Smooth PDE-Constrained Problems
Marco Bernreuther, Michael Dellnitz, Bennet Gebken +4
Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimizati…
Using second-order information in gradient sampling methods for nonsmooth optimization
Bennet Gebken
In this article, we introduce a novel concept for second-order information of a nonsmooth function inspired by the Goldstein eps-subdifferential. It comprises the coefficients of a…
On the structure of regularization paths for piecewise differentiable regularization terms
Bennet Gebken, Katharina Bieker, Sebastian Peitz
Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity.…
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…
A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems
Bennet Gebken, Sebastian Peitz, Michael Dellnitz
In this article we propose a descent method for equality and inequality constrained multiobjective optimization problems (MOPs) which generalizes the steepest descent method for un…