A Lyusternik–Graves theorem for the proximal point method
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http://hdl.handle.net/10045/29039
| Title: | A Lyusternik–Graves theorem for the proximal point method |
|---|---|
| Authors: | Aragón Artacho, Francisco Javier | Gaydu, Michaël |
| Research Group/s: | Laboratorio de Optimización (LOPT) |
| Center, Department or Service: | Universidad de Alicante. Departamento de Estadística e Investigación Operativa |
| Keywords: | Proximal point algorithm | Generalized equations | Perturbations | Metric regularity | Strong regularity |
| Knowledge Area: | Estadística e Investigación Operativa | Análisis Matemático |
| Issue Date: | 1-Oct-2011 |
| Publisher: | Springer Science+Business Media, LLC |
| Citation: | ARAGÓN ARTACHO, Francisco J.; GAYDU, Michaël. "A Lyusternik–Graves theorem for the proximal point method". Computational Optimization and Applications. Vol. 52, Issue 3 (July 2012). ISSN 0926-6003, pp. 785-803 |
| Abstract: | We consider a generalized version of the proximal point algorithm for solving the perturbed inclusion y∈T(x), where y is a perturbation element near 0 and T is a set-valued mapping acting from a Banach space X to a Banach space Y which is metrically regular around some point (xˉ,0) in its graph. We study the behavior of the convergent iterates generated by the algorithm and we prove that they inherit the regularity properties of T, and vice versa. We analyze the cases when the mapping T is metrically regular and strongly regular. |
| Sponsor: | Research of the first author was partially supported by Ministerio de Ciencia e Innovación (Spain), grant MTM2008-06695-C03-01 and program “Juan de la Cierva”. Research of the second author was partially supported by Contract EA4540 (France). |
| URI: | http://hdl.handle.net/10045/29039 |
| ISSN: | 0926-6003 (Print) | 1573-2894 (Online) |
| DOI: | 10.1007/s10589-011-9439-6 |
| Language: | eng |
| Type: | info:eu-repo/semantics/article |
| Rights: | The original publication is available at www.springerlink.com |
| Peer Review: | si |
| Publisher version: | http://dx.doi.org/10.1007/s10589-011-9439-6 |
| Appears in Collections: | INV - LOPT - Artículos de Revistas |
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| File | Description | Size | Format | |
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 2012_Aragon_Gaydu_ComputOptimAppl.pdf | Preprint (acceso abierto) | 190,7 kB | Adobe PDF | Open Preview |
 2012_Aragon_Gaydu_ComputOptimAppl_final.pdf | Versión final (acceso restringido) | 623,26 kB | Adobe PDF | Open Request a copy |
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