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.

Optimization and Control (math.OC); Machine Learning (cs.LG)

arXiv:2510.19341 [math.OC]

(or arXiv:2510.19341v3 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2510.19341 Focus to learn more arXiv-issued DOI via DataCite

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