An Application of Proof Mining to the Proximal Point Algorithm in CAT(0) Spaces

Abstract

Mathematics Almost Everywhere, pp. 153-167 (2018) No AccessChapter 8: An Application of Proof Mining to the Proximal Point Algorithm in CAT(0) SpacesLaurenţiu Leuştean and Andrei SipoşLaurenţiu LeuşteanFaculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, 010014 Bucharest, RomaniaSimion Stoilow Institute of Mathematics of the Romanian Academy, P. O. Box 1-764, 014700 Bucharest, Romania and Andrei SipoşFaculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, 010014 Bucharest, RomaniaSimion Stoilow Institute of Mathematics of the Romanian Academy, P. O. Box 1-764, 014700 Bucharest, Romaniahttps://doi.org/10.1142/9789813237315_0008Cited by:2 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: We compute, using techniques originally introduced by Kohlenbach, the first author and Nicolae, uniform rates of metastability for the proximal point algorithm in the context of CAT(0) spaces (as first considered by Bačák), specifically for the case where the ambient space is totally bounded. This result is part of the program of proof mining, which aims to apply methods of mathematical logic with the purpose of extracting quantitative information out of ordinary mathematical proofs, which may not be necessarily constructive. Dedication: Dedicated to the memory of Professor Solomon Marcus (1925–2016) FiguresReferencesRelatedDetailsCited By 2Quantitative results on a Halpern-type proximal point algorithmLaurenţiu Leuştean and Pedro Pinto25 February 2021 | Computational Optimization and Applications, Vol. 79, No. 1A Rate of Metastability for the Halpern Type Proximal Point AlgorithmPedro Pinto10 February 2021 | Numerical Functional Analysis and Optimization, Vol. 42, No. 3 Mathematics Almost EverywhereMetrics History PDF download

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