{"ID":2851584,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.19341","arxiv_id":"2510.19341","title":"Nonmonotone subgradient methods based on a local descent lemma","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2510.19341","url_pdf":"https://arxiv.org/pdf/2510.19341v2","authors":"[\"Francisco J. Aragón-Artacho\",\"Rubén Campoy\",\"Pedro Pérez-Aros\",\"David Torregrosa-Belén\"]","published":"2025-10-22T08:06:40Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.LG\"]","methods":"[]","has_code":false}