5 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…
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…