Superlinear convergence in nonsmooth optimization via higher-order cutting-plane models
Abstract
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 convergence (of serious steps) to a minimum. In smooth optimization, superlinear convergence can be achieved by using higher-order models. We show that the same is true for the nonsmooth case, i.e., we show that cutting-plane models involving higher-order expansions can be used to achieve superlinear convergence in nonsmooth optimization. We first formally define higher-order cutting-plane models for lower- functions and derive an error estimate. Afterwards, we construct a trust-region bundle method based on these models that achieves local superlinear convergence of serious steps, and overall superlinear convergence for certain finite max-type functions. Finally, we verify the superlinear convergence in numerical experiments.
Cite
@article{arxiv.2603.23236,
title = {Superlinear convergence in nonsmooth optimization via higher-order cutting-plane models},
author = {Bennet Gebken and Michael Ulbrich},
journal= {arXiv preprint arXiv:2603.23236},
year = {2026}
}