---
_id: '51208'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>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 weakly lower semismooth
    functions which is able to compute new subgradients that improve a given approximation
    in case a direction with insufficient descent was computed. Combined with a recently
    proposed deterministic gradient sampling approach, this yields a deterministic
    and provably convergent way to approximate subdifferentials for computing descent
    directions.</jats:p>
author:
- first_name: Bennet
  full_name: Gebken, Bennet
  id: '32643'
  last_name: Gebken
citation:
  ama: Gebken B. A note on the convergence of deterministic gradient sampling in nonsmooth
    optimization. <i>Computational Optimization and Applications</i>. Published online
    2024. doi:<a href="https://doi.org/10.1007/s10589-024-00552-0">10.1007/s10589-024-00552-0</a>
  apa: Gebken, B. (2024). A note on the convergence of deterministic gradient sampling
    in nonsmooth optimization. <i>Computational Optimization and Applications</i>.
    <a href="https://doi.org/10.1007/s10589-024-00552-0">https://doi.org/10.1007/s10589-024-00552-0</a>
  bibtex: '@article{Gebken_2024, title={A note on the convergence of deterministic
    gradient sampling in nonsmooth optimization}, DOI={<a href="https://doi.org/10.1007/s10589-024-00552-0">10.1007/s10589-024-00552-0</a>},
    journal={Computational Optimization and Applications}, publisher={Springer Science
    and Business Media LLC}, author={Gebken, Bennet}, year={2024} }'
  chicago: Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling
    in Nonsmooth Optimization.” <i>Computational Optimization and Applications</i>,
    2024. <a href="https://doi.org/10.1007/s10589-024-00552-0">https://doi.org/10.1007/s10589-024-00552-0</a>.
  ieee: 'B. Gebken, “A note on the convergence of deterministic gradient sampling
    in nonsmooth optimization,” <i>Computational Optimization and Applications</i>,
    2024, doi: <a href="https://doi.org/10.1007/s10589-024-00552-0">10.1007/s10589-024-00552-0</a>.'
  mla: Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling
    in Nonsmooth Optimization.” <i>Computational Optimization and Applications</i>,
    Springer Science and Business Media LLC, 2024, doi:<a href="https://doi.org/10.1007/s10589-024-00552-0">10.1007/s10589-024-00552-0</a>.
  short: B. Gebken, Computational Optimization and Applications (2024).
date_created: 2024-02-07T07:23:23Z
date_updated: 2024-02-08T08:05:54Z
department:
- _id: '101'
doi: 10.1007/s10589-024-00552-0
keyword:
- Applied Mathematics
- Computational Mathematics
- Control and Optimization
language:
- iso: eng
publication: Computational Optimization and Applications
publication_identifier:
  issn:
  - 0926-6003
  - 1573-2894
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: A note on the convergence of deterministic gradient sampling in nonsmooth optimization
type: journal_article
user_id: '32643'
year: '2024'
...