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dc.creator Leustean, Laurentiu es
dc.creator Nicolae, Adriana es
dc.creator Sipos, Andrei es
dc.date.accessioned 2018-10-10T07:06:49Z
dc.date.available 2018-10-10T07:06:49Z
dc.date.issued 2018
dc.identifier.issn 0925-5001 es
dc.identifier.issn 1573-2916 es
dc.identifier.uri https://hdl.handle.net/11441/79258
dc.description.abstract The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions. The algorithm works by applying successively so-called “resolvent” mappings associated to the original object that one aims to optimize. In this paper we abstract from the corresponding resolvents employed in these problems the natural notion of jointly firmly nonexpansive families of mappings. This leads to a streamlined method of proving weak convergence of this class of algorithms in the context of complete CAT(0) spaces (and hence also in Hilbert spaces). In addition, we consider the notion of uniform firm nonexpansivity in order to similarly provide a unified presentation of a case where the algorithm converges strongly. Methods which stem from proof mining, an applied subfield of logic, yield in this situation computable and low-complexity rates of convergence. es
dc.description.sponsorship Dirección General de Enseñanza Superior (Ministerio de Economía y Competitividad) es
dc.description.sponsorship Romanian National Authority for Scientific Research es
dc.format application/pdf es
dc.language.iso eng es
dc.publisher Springer es
dc.relation.ispartof Journal of Global Optimization, 1-25.
dc.rights Attribution-NonCommercial-NoDerivatives 4.0 Internacional *
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/ *
dc.subject Convex optimization es
dc.subject Proximal point algorithm es
dc.subject CAT(0) spaces es
dc.subject Jointly firmly nonexpansive families es
dc.subject Uniformly firmly nonexpansive mappings es
dc.subject Proof mining es
dc.subject Rates of convergence es
dc.title An abstract proximal point algorithm es
dc.type info:eu-repo/semantics/article es
dc.type.version info:eu-repo/semantics/submittedVersion es
dc.rights.accessrights info:eu-repo/semantics/openAccess es
dc.contributor.affiliation Universidad de Sevilla. Departamento de Análisis Matemático es
dc.relation.projectID MTM2015-65242-C2-1-P es
dc.relation.projectID PN-II-ID-PCE-2011-3-0383 es
dc.relation.publisherversion https://link.springer.com/content/pdf/10.1007%2Fs10898-018-0655-9.pdf es
dc.identifier.doi 10.1007/s10898-018-0655-9 es
dc.contributor.group Universidad de Sevilla. FQM127: Análisis Funcional no Lineal es
idus.format.extent 23 p. es
dc.journaltitle Journal of Global Optimization es
dc.publication.initialPage 1 es
dc.publication.endPage 25 es
dc.contributor.funder Ministerio de Economía y Competitividad (MINECO). España
dc.contributor.funder Romanian National Authority for Scientific Research
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