Título:	Accelerated derivative-free spectral residual method for nonlinear systems of equations
Autor(es):	Birgin, Ernesto G. Gardenghi, John Lenon Cardoso Marcondes, Diaulas S. Martínez, José Mario
ORCID:	https://orcid.org/0000-0002-7466-7663
Afiliação do autor:	University of São Paulo, Institute of Mathematics and Statistics, Department of Computer Science University of Brasília, Faculty of Sciences and Technologies in Engineering University of São Paulo, Institute of Mathematics and Statistics, Department of Applied Mathematics State University of Campinas, Institute of Mathematics, Statistics and Scientific Computing, Department of Applied Mathematics
Assunto:	Métodos de resíduos espectrais Equações não-lineares Algoritmos
Data de publicação:	17-Fev-2025
Editora:	EDP Sciences
Referência:	BIRGIN, Ernesto G. et al. Accelerated derivative-free spectral residual method for nonlinear systems of equations. RAIRO - Operations Research, [S. l.], v. 59, n. 1, p. 609-624, Jan./Feb. 2025. DOI: https://doi.org/10.1051/ro/2024234. Disponível em: https://www.rairo-ro.org/articles/ro/abs/2025/01/ro240062/ro240062.html. Acesso em: 14 mar. 2025.
Abstract:	Many continuous models of natural phenomena require the solution of large-scale nonlinear systems of equations. For example, the discretization of many partial differential equations, which are widely used in physics, chemistry, and engineering, requires the solution of subproblems in which a nonlinear algebraic system has to be addressed, especially one in which stable implicit difference schemes are used. Spectral residual methods are powerful tools for solving nonlinear systems of equations without derivatives. In a recent paper [Birgin and Martínez, SIAM J. Numer. Anal. 60 (2022) 3145–3180], it was shown that an acceleration technique based on the Sequential Secant Method can greatly improve its efficiency and robustness. In the present work, an R implementation of the method is presented. Numerical experiments with a widely used test bed compare the presented approach with its plain (i.e., non-accelerated) version that is part of the R package BB. Additional numerical experiments compare the proposed method with NITSOL, a state-of-the-art solver for nonlinear systems. These comparisons show that the acceleration process greatly improves the robustness of its counterpart included in the existing R package. As a by-product, an interface is provided between R and the consolidated CUTEst collection, which contains over a thousand nonlinear programming problems of all types and represents a standard for evaluating the performance of optimization methods.
Unidade Acadêmica:	Faculdade de Ciências e Tecnologias em Engenharia (FCTE) – Campus UnB Gama
Licença:	This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
DOI:	https://doi.org/10.1051/ro/2024234
Versão da editora:	https://www.rairo-ro.org/component/article?access=doi&doi=10.1051/ro/2024234
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