Using second-order information in gradient sampling methods for nonsmooth optimization
Optimization and Control
2025-01-06 v4
Abstract
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 all existing second-order Taylor expansions in an eps-ball around a given point. Based on this concept, we define a model of the objective as the maximum of these Taylor expansions, and derive a sampling scheme for its approximation in practice. Minimization of this model induces a simple descent method, for which we show convergence for the case where the objective is convex or of max-type. While we do not prove any rate of convergence of this method, numerical experiments suggest superlinear behavior with respect to the number of oracle calls of the objective.
Cite
@article{arxiv.2210.04579,
title = {Using second-order information in gradient sampling methods for nonsmooth optimization},
author = {Bennet Gebken},
journal= {arXiv preprint arXiv:2210.04579},
year = {2025}
}