The modified proximal point algorithm in Hadamard spaces

The purpose of this paper is to propose a modified proximal point algorithm for solving minimization problems in Hadamard spaces. We then prove that the sequence generated by the algorithm converges strongly (convergence in metric) to a minimizer of convex objective functions. The results extend sev...

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Detalles Bibliográficos
Autores principales: Chang, Shih-sen, Wang, Lin, Wen, Ching-Feng, Zhang, Jian Qiang
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5968084/
https://www.ncbi.nlm.nih.gov/pubmed/30137867
http://dx.doi.org/10.1186/s13660-018-1713-z
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author Chang, Shih-sen
Wang, Lin
Wen, Ching-Feng
Zhang, Jian Qiang
author_facet Chang, Shih-sen
Wang, Lin
Wen, Ching-Feng
Zhang, Jian Qiang
author_sort Chang, Shih-sen
collection PubMed
description The purpose of this paper is to propose a modified proximal point algorithm for solving minimization problems in Hadamard spaces. We then prove that the sequence generated by the algorithm converges strongly (convergence in metric) to a minimizer of convex objective functions. The results extend several results in Hilbert spaces, Hadamard manifolds and non-positive curvature metric spaces.
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spelling pubmed-59680842018-06-21 The modified proximal point algorithm in Hadamard spaces Chang, Shih-sen Wang, Lin Wen, Ching-Feng Zhang, Jian Qiang J Inequal Appl Research The purpose of this paper is to propose a modified proximal point algorithm for solving minimization problems in Hadamard spaces. We then prove that the sequence generated by the algorithm converges strongly (convergence in metric) to a minimizer of convex objective functions. The results extend several results in Hilbert spaces, Hadamard manifolds and non-positive curvature metric spaces. Springer International Publishing 2018-05-24 2018 /pmc/articles/PMC5968084/ /pubmed/30137867 http://dx.doi.org/10.1186/s13660-018-1713-z Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Chang, Shih-sen
Wang, Lin
Wen, Ching-Feng
Zhang, Jian Qiang
The modified proximal point algorithm in Hadamard spaces
title The modified proximal point algorithm in Hadamard spaces
title_full The modified proximal point algorithm in Hadamard spaces
title_fullStr The modified proximal point algorithm in Hadamard spaces
title_full_unstemmed The modified proximal point algorithm in Hadamard spaces
title_short The modified proximal point algorithm in Hadamard spaces
title_sort modified proximal point algorithm in hadamard spaces
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5968084/
https://www.ncbi.nlm.nih.gov/pubmed/30137867
http://dx.doi.org/10.1186/s13660-018-1713-z
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