Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1058702018, G106083612, G1175115578, FROM DETERMINISTIC TO RANDOM AND STOCHASTIC SWEEPING PROCESSES, G1909218897, G2262748287, VARIATIONAL ANALYSIS OF GENERALIZED SUPREMUM FUNCTION WITH APPLICATIONS, G294895050, G300979063, G3480869486, G3620625767, G3804928816, G410571670, G425668148, G451917667, G5080475149, G523076202, G5245394943, NONCONVEX SPLITTING METHODS WITH APPLICATIONS TO EUCLIDEAN DISTANCE MATRIX COMPLETION, G5539308778, G5600382928, G5967599077, G6033112984, ON GEOMETRIC AND VARIATIONAL PROPERTIES OF PROBUST CHANCE CONSTRAINED OPTIMIZATION PROBLEMS, G7084143925, A NEW PROBABILISTIC PARADIGM FOR MODELLING OPTIMAL DECISION-MAKING PROCESSES UNDER UNCERTAINTY, CENTER FOR MATHEMATICAL MODELING (CMM), CENTRO DE MODELAMIENTO MATEMATICO
OpenAlex ID: W4416246761
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