Using second-order information in gradient sampling methods for nonsmooth optimization
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866909447209615360 |
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| author | Gebken, Bennet |
| author_facet | Gebken, Bennet |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_04579 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Using second-order information in gradient sampling methods for nonsmooth optimization Gebken, Bennet Optimization and Control 90C56, 90C30, 49J52 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. |
| title | Using second-order information in gradient sampling methods for nonsmooth optimization |
| topic | Optimization and Control 90C56, 90C30, 49J52 |
| url | https://arxiv.org/abs/2210.04579 |