---
_id: '34618'
abstract:
- lang: eng
  text: "In this article, we show how second-order derivative information can be\r\nincorporated
    into gradient sampling methods for nonsmooth optimization. The\r\nsecond-order
    information we consider is essentially the set of coefficients of\r\nall second-order
    Taylor expansions of the objective in a closed ball around a\r\ngiven point. Based
    on this concept, we define a model of the objective as the\r\nmaximum of these
    Taylor expansions. Iteratively minimizing this model\r\n(constrained to the closed
    ball) results in a simple descent method, for which\r\nwe prove convergence to
    minimal points in case the objective is convex. To\r\nobtain an implementable
    method, we construct an approximation scheme for the\r\nsecond-order information
    based on sampling objective values, gradients and\r\nHessian matrices at finitely
    many points. Using a set of test problems, we\r\ncompare the resulting method
    to five other available solvers. Considering the\r\nnumber of function evaluations,
    the results suggest that the method we propose\r\nis superior to the standard
    gradient sampling method, and competitive compared\r\nto other methods."
author:
- first_name: Bennet
  full_name: Gebken, Bennet
  id: '32643'
  last_name: Gebken
citation:
  ama: Gebken B. Using second-order information in gradient sampling methods for 
    nonsmooth optimization. <i>arXiv:221004579</i>. Published online 2022.
  apa: Gebken, B. (2022). Using second-order information in gradient sampling methods
    for  nonsmooth optimization. In <i>arXiv:2210.04579</i>.
  bibtex: '@article{Gebken_2022, title={Using second-order information in gradient
    sampling methods for  nonsmooth optimization}, journal={arXiv:2210.04579}, author={Gebken,
    Bennet}, year={2022} }'
  chicago: Gebken, Bennet. “Using Second-Order Information in Gradient Sampling Methods
    for  Nonsmooth Optimization.” <i>ArXiv:2210.04579</i>, 2022.
  ieee: B. Gebken, “Using second-order information in gradient sampling methods for 
    nonsmooth optimization,” <i>arXiv:2210.04579</i>. 2022.
  mla: Gebken, Bennet. “Using Second-Order Information in Gradient Sampling Methods
    for  Nonsmooth Optimization.” <i>ArXiv:2210.04579</i>, 2022.
  short: B. Gebken, ArXiv:2210.04579 (2022).
date_created: 2022-12-20T15:25:17Z
date_updated: 2022-12-20T15:28:54Z
department:
- _id: '101'
external_id:
  arxiv:
  - '2210.04579'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/pdf/2210.04579
oa: '1'
publication: arXiv:2210.04579
status: public
title: Using second-order information in gradient sampling methods for  nonsmooth
  optimization
type: preprint
user_id: '32643'
year: '2022'
...