Global behavior of the Douglas–Rachford method for a nonconvex feasibility problem
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Title: | Global behavior of the Douglas–Rachford method for a nonconvex feasibility problem |
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Authors: | Aragón Artacho, Francisco Javier | Borwein, Jonathan M. | Tam, Matthew K. |
Research Group/s: | Laboratorio de Optimización (LOPT) |
Center, Department or Service: | Universidad de Alicante. Departamento de Matemáticas |
Keywords: | Douglas–Rachford algorithm | Global convergence | Feasibility problem | Half-space | Non-convex |
Knowledge Area: | Estadística e Investigación Operativa |
Issue Date: | Jun-2016 |
Publisher: | Springer Science+Business Media New York |
Citation: | Journal of Global Optimization. 2016, 65(2): 309-327. doi:10.1007/s10898-015-0380-6 |
Abstract: | In recent times the Douglas–Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems current theory is not sufficient to explain this observed success and is mainly concerned with questions of local convergence. In this paper we analyze global behavior of the method for finding a point in the intersection of a half-space and a potentially non-convex set which is assumed to satisfy a well-quasi-ordering property or a property weaker than compactness. In particular, the special case in which the second set is finite is covered by our framework and provides a prototypical setting for combinatorial optimization problems. |
Sponsor: | F.J. Aragón Artacho was supported by MINECO of Spain and FEDER of EU, as part of the Ramón y Cajal program (RYC-2013-13327) and the Grant MTM2014-59179-C2-1-P. J.M. Borwein was supported, in part, by the Australian Research Council. M.K. Tam was supported by an Australian Post-Graduate Award. |
URI: | http://hdl.handle.net/10045/55937 |
ISSN: | 0925-5001 (Print) | 1573-2916 (Online) |
DOI: | 10.1007/s10898-015-0380-6 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | © Springer Science+Business Media New York 2015. The final publication is available at Springer via http://dx.doi.org/10.1007/s10898-015-0380-6 |
Peer Review: | si |
Publisher version: | http://dx.doi.org/10.1007/s10898-015-0380-6 |
Appears in Collections: | INV - LOPT - Artículos de Revistas |
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2016_Aragon_etal_JGlobOptim_final.pdf | Versión final (acceso restringido) | 493,54 kB | Adobe PDF | Open Request a copy |
2016_Aragon_etal_JGlobOptim_preprint.pdf | Preprint (acceso abierto) | 197,34 kB | Adobe PDF | Open Preview |
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