Using Positive Spanning Sets to Achieve d-Stationarity with the Boosted DC Algorithm
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Título: | Using Positive Spanning Sets to Achieve d-Stationarity with the Boosted DC Algorithm |
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Autor/es: | Aragón Artacho, Francisco Javier | Campoy, Rubén | Vuong, Phan T. |
Grupo/s de investigación o GITE: | Laboratorio de Optimización (LOPT) |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Matemáticas |
Palabras clave: | Difference of convex functions | Boosted difference of convex functions algorithm | Positive spanning sets | d-Stationary points | Derivative-free optimization |
Área/s de conocimiento: | Estadística e Investigación Operativa |
Fecha de publicación: | jun-2020 |
Editor: | Springer Nature |
Cita bibliográfica: | Vietnam Journal of Mathematics. 2020, 48: 363-376. doi:10.1007/s10013-020-00400-8 |
Resumen: | The Difference of Convex functions Algorithm (DCA) is widely used for minimizing the difference of two convex functions. A recently proposed accelerated version, termed BDCA for Boosted DC Algorithm, incorporates a line search step to achieve a larger decrease of the objective value at each iteration. Thanks to this step, BDCA usually converges much faster than DCA in practice. The solutions found by DCA are guaranteed to be critical points of the problem, but these may not be local minima. Although BDCA tends to improve the objective value of the solutions it finds, these are frequently just critical points as well. In this paper we combine BDCA with a simple Derivative-Free Optimization (DFO) algorithm to force the d-stationarity (lack of descent direction) at the point obtained. The potential of this approach is illustrated through some computational experiments on a Minimum-Sum-of-Squares clustering problem. Our numerical results demonstrate that the new method provides better solutions while still remains faster than DCA in the majority of test cases. |
Patrocinador/es: | The first author was supported by MINECO of Spain and ERDF of EU, as part of the Ramón y Cajal program (RYC-2013-13327) and the grants MTM2014-59179-C2-1-P and PGC2018-097960-B-C22. The second author was supported by MINECO of Spain and ESF of EU under the program “Ayudas para contratos predoctorales para la formación de doctores 2015” (BES-2015-073360). The last author was supported by FWF (Austrian Science Fund), project M2499-N32 and Vietnam National Foundation for Science and Technology Development (NAFOSTED) project 101.01-2019.320. |
URI: | http://hdl.handle.net/10045/107394 |
ISSN: | 2305-221X (Print) | 2305-2228 (Online) |
DOI: | 10.1007/s10013-020-00400-8 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | © The Author(s) 2020, corrected publication April 2020. 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 weremade. 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://creativecommonshorg/licenses/by/4.0/. |
Revisión científica: | si |
Versión del editor: | https://doi.org/10.1007/s10013-020-00400-8 |
Aparece en las colecciones: | INV - LOPT - Artículos de Revistas |
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