Nonmonotone subgradient methods based on a local descent lemma
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917424027140096 |
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| author | Aragón-Artacho, Francisco J. Campoy, Rubén Pérez-Aros, Pedro Torregrosa-Belén, David |
| author_facet | Aragón-Artacho, Francisco J. Campoy, Rubén Pérez-Aros, Pedro Torregrosa-Belén, David |
| contents | In this paper we present a nonmonotone line search subgradient algorithm tailored to upper-$\mathcal{C}^2$ functions. This is a family of nonsmooth and nonconvex functions that satisfies a nonsmooth and local version of the descent lemma, making them suitable for line searches. We prove subsequential convergence of the proposed algorithm to a stationary point of the optimization problem. Our approach allows us to cover the setting of various subgradient algorithms, including Newton and quasi-Newton methods. In addition, we propose a specification of the general scheme, named Self-adaptive Nonmonotone Subgradient Method (SNSM), which automatically updates the parameters of the line search. Particular attention is paid to the minimum sum-of-squares clustering problem, for which we provide a concrete implementation of SNSM. We conclude with some numerical experiments where we exhibit the advantages of SNSM in comparison with some known algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19341 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonmonotone subgradient methods based on a local descent lemma Aragón-Artacho, Francisco J. Campoy, Rubén Pérez-Aros, Pedro Torregrosa-Belén, David Optimization and Control Machine Learning 90C26, 90C30, 90C53, 49J52, 65K05 In this paper we present a nonmonotone line search subgradient algorithm tailored to upper-$\mathcal{C}^2$ functions. This is a family of nonsmooth and nonconvex functions that satisfies a nonsmooth and local version of the descent lemma, making them suitable for line searches. We prove subsequential convergence of the proposed algorithm to a stationary point of the optimization problem. Our approach allows us to cover the setting of various subgradient algorithms, including Newton and quasi-Newton methods. In addition, we propose a specification of the general scheme, named Self-adaptive Nonmonotone Subgradient Method (SNSM), which automatically updates the parameters of the line search. Particular attention is paid to the minimum sum-of-squares clustering problem, for which we provide a concrete implementation of SNSM. We conclude with some numerical experiments where we exhibit the advantages of SNSM in comparison with some known algorithms. |
| title | Nonmonotone subgradient methods based on a local descent lemma |
| topic | Optimization and Control Machine Learning 90C26, 90C30, 90C53, 49J52, 65K05 |
| url | https://arxiv.org/abs/2510.19341 |