A Direct Proof of Convergence of Davis–Yin Splitting Algorithm Allowing Larger Stepsizes
Por favor, use este identificador para citar o enlazar este ítem:
http://hdl.handle.net/10045/121869
Título: | A Direct Proof of Convergence of Davis–Yin Splitting Algorithm Allowing Larger Stepsizes |
---|---|
Autor/es: | Aragón Artacho, Francisco Javier | Torregrosa-Belén, David |
Grupo/s de investigación o GITE: | Laboratorio de Optimización (LOPT) |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Matemáticas |
Palabras clave: | Monotone inclusion | Resolvent | Splitting algorithm | Forward-backward | Strengthening |
Área/s de conocimiento: | Estadística e Investigación Operativa |
Fecha de publicación: | 26-feb-2022 |
Editor: | Springer Nature |
Cita bibliográfica: | Set-Valued and Variational Analysis. 2022, 30: 1011-1029. https://doi.org/10.1007/s11228-022-00631-6 |
Resumen: | This note is devoted to the splitting algorithm proposed by Davis and Yin (Set-valued Var. Anal. 25(4), 829–858, 2017) for computing a zero of the sum of three maximally monotone operators, with one of them being cocoercive. We provide a direct proof that guarantees its convergence when the stepsizes are smaller than four times the cocoercivity constant, thus doubling the size of the interval established by Davis and Yin. As a by-product, the same conclusion applies to the forward-backward splitting algorithm. Further, we use the notion of “strengthening” of a set-valued operator to derive a new splitting algorithm for computing the resolvent of the sum. Last but not least, we provide some numerical experiments illustrating the importance of appropriately choosing the stepsize and relaxation parameters of the algorithms. |
Patrocinador/es: | FJAA and DTB were partially supported by the Ministry of Science, Innovation and Universities of Spain and the European Regional Development Fund (ERDF) of the European Commission, Grant PGC2018-097960-B-C22. FJAA was partially supported by the Generalitat Valenciana (AICO/2021/165). DTB was supported by MINECO and European Social Fund (PRE2019-090751) under the program “Ayudas para contratos predoctorales para la formación de doctores” 2019. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. |
URI: | http://hdl.handle.net/10045/121869 |
ISSN: | 1877-0533 (Print) | 1877-0541 (Online) |
DOI: | 10.1007/s11228-022-00631-6 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | © The Author(s) 2022. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Revisión científica: | si |
Versión del editor: | https://doi.org/10.1007/s11228-022-00631-6 |
Aparece en las colecciones: | INV - LOPT - Artículos de Revistas |
Archivos en este ítem:
Archivo | Descripción | Tamaño | Formato | |
---|---|---|---|---|
Aragon_Torregrosa_2022_Set-ValuedVarAnal.pdf | 1,08 MB | Adobe PDF | Abrir Vista previa | |
Este ítem está licenciado bajo Licencia Creative Commons