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A primal-dual algorithm framework for convex saddle-point optimization
In this study, we introduce a primal-dual prediction-correction algorithm framework for convex optimization problems with known saddle-point structure. Our unified frame adds the proximal term with a positive definite weighting matrix. Moreover, different proximal parameters in the frame can derive...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer International Publishing
2017
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5656743/ https://www.ncbi.nlm.nih.gov/pubmed/29104405 http://dx.doi.org/10.1186/s13660-017-1548-z |
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author | Zhang, Benxin Zhu, Zhibin |
author_facet | Zhang, Benxin Zhu, Zhibin |
author_sort | Zhang, Benxin |
collection | PubMed |
description | In this study, we introduce a primal-dual prediction-correction algorithm framework for convex optimization problems with known saddle-point structure. Our unified frame adds the proximal term with a positive definite weighting matrix. Moreover, different proximal parameters in the frame can derive some existing well-known algorithms and yield a class of new primal-dual schemes. We prove the convergence of the proposed frame from the perspective of proximal point algorithm-like contraction methods and variational inequalities approach. The convergence rate [Formula: see text] in the ergodic and nonergodic senses is also given, where t denotes the iteration number. |
format | Online Article Text |
id | pubmed-5656743 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2017 |
publisher | Springer International Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-56567432017-11-01 A primal-dual algorithm framework for convex saddle-point optimization Zhang, Benxin Zhu, Zhibin J Inequal Appl Research In this study, we introduce a primal-dual prediction-correction algorithm framework for convex optimization problems with known saddle-point structure. Our unified frame adds the proximal term with a positive definite weighting matrix. Moreover, different proximal parameters in the frame can derive some existing well-known algorithms and yield a class of new primal-dual schemes. We prove the convergence of the proposed frame from the perspective of proximal point algorithm-like contraction methods and variational inequalities approach. The convergence rate [Formula: see text] in the ergodic and nonergodic senses is also given, where t denotes the iteration number. Springer International Publishing 2017-10-25 2017 /pmc/articles/PMC5656743/ /pubmed/29104405 http://dx.doi.org/10.1186/s13660-017-1548-z Text en © The Author(s) 2017 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 Zhang, Benxin Zhu, Zhibin A primal-dual algorithm framework for convex saddle-point optimization |
title | A primal-dual algorithm framework for convex saddle-point optimization |
title_full | A primal-dual algorithm framework for convex saddle-point optimization |
title_fullStr | A primal-dual algorithm framework for convex saddle-point optimization |
title_full_unstemmed | A primal-dual algorithm framework for convex saddle-point optimization |
title_short | A primal-dual algorithm framework for convex saddle-point optimization |
title_sort | primal-dual algorithm framework for convex saddle-point optimization |
topic | Research |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5656743/ https://www.ncbi.nlm.nih.gov/pubmed/29104405 http://dx.doi.org/10.1186/s13660-017-1548-z |
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