Loading…

Convergence of the reweighted sub(1) minimization algorithm for sub(2)- sub( )pminimization

The iteratively reweighted sub(1) minimization algorithm (IRL1) has been widely used for variable selection, signal reconstruction and image processing. In this paper, we show that any sequence generated by the IRL1 is bounded and any accumulation point is a stationary point of the sub(2)- sub( )pmi...

Full description

Saved in:
Bibliographic Details
Published in:Computational optimization and applications 2014-10, Vol.59 (1-2), p.47-61
Main Authors: Chen, Xiaojun, Zhou, Weijun
Format: Article
Language:English
Subjects:
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page 61
container_issue 1-2
container_start_page 47
container_title Computational optimization and applications
container_volume 59
creator Chen, Xiaojun
Zhou, Weijun
description The iteratively reweighted sub(1) minimization algorithm (IRL1) has been widely used for variable selection, signal reconstruction and image processing. In this paper, we show that any sequence generated by the IRL1 is bounded and any accumulation point is a stationary point of the sub(2)- sub( )pminimization problem with 0
doi_str_mv 10.1007/s10589-013-9553-8
format article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_miscellaneous_1671583635</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1671583635</sourcerecordid><originalsourceid>FETCH-proquest_miscellaneous_16715836353</originalsourceid><addsrcrecordid>eNqVyrsKwjAUANAgCtbHB7hltEP0pjFtM4viB7g5SNXbNtImmqQKfr0gDq5OZzmEzDgsOEC29BxkrhhwwZSUguU9EnGZCZbkatUnEagkZSmAGJKR91cAUJlIInJYW_NAV6E5I7UlDTVSh0_UVR3wQn13mvOYttroVr-KoK2hRVNZp0Pd0tK6z0hi9pHGt985IYOyaDxOv47JfLvZr3fs5uy9Qx-OrfZnbJrCoO38kacZl7lIhRR_1DcYWEzU</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1671583635</pqid></control><display><type>article</type><title>Convergence of the reweighted sub(1) minimization algorithm for sub(2)- sub( )pminimization</title><source>ABI/INFORM Collection</source><source>Business Source Ultimate【Trial: -2024/12/31】【Remote access available】</source><source>Springer Link</source><creator>Chen, Xiaojun ; Zhou, Weijun</creator><creatorcontrib>Chen, Xiaojun ; Zhou, Weijun</creatorcontrib><description>The iteratively reweighted sub(1) minimization algorithm (IRL1) has been widely used for variable selection, signal reconstruction and image processing. In this paper, we show that any sequence generated by the IRL1 is bounded and any accumulation point is a stationary point of the sub(2)- sub( )pminimization problem with 0&lt;p&lt;1. Moreover, the stationary point is a global minimizer and the convergence rate is approximately linear under certain conditions. We derive posteriori error bounds which can be used to construct practical stopping rules for the algorithm.</description><identifier>ISSN: 0926-6003</identifier><identifier>EISSN: 1573-2894</identifier><identifier>DOI: 10.1007/s10589-013-9553-8</identifier><language>eng</language><subject>Algorithms ; Construction ; Convergence ; Image processing ; Mathematical models ; Minimization ; Optimization ; Signal reconstruction</subject><ispartof>Computational optimization and applications, 2014-10, Vol.59 (1-2), p.47-61</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925,36061</link.rule.ids></links><search><creatorcontrib>Chen, Xiaojun</creatorcontrib><creatorcontrib>Zhou, Weijun</creatorcontrib><title>Convergence of the reweighted sub(1) minimization algorithm for sub(2)- sub( )pminimization</title><title>Computational optimization and applications</title><description>The iteratively reweighted sub(1) minimization algorithm (IRL1) has been widely used for variable selection, signal reconstruction and image processing. In this paper, we show that any sequence generated by the IRL1 is bounded and any accumulation point is a stationary point of the sub(2)- sub( )pminimization problem with 0&lt;p&lt;1. Moreover, the stationary point is a global minimizer and the convergence rate is approximately linear under certain conditions. We derive posteriori error bounds which can be used to construct practical stopping rules for the algorithm.</description><subject>Algorithms</subject><subject>Construction</subject><subject>Convergence</subject><subject>Image processing</subject><subject>Mathematical models</subject><subject>Minimization</subject><subject>Optimization</subject><subject>Signal reconstruction</subject><issn>0926-6003</issn><issn>1573-2894</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNqVyrsKwjAUANAgCtbHB7hltEP0pjFtM4viB7g5SNXbNtImmqQKfr0gDq5OZzmEzDgsOEC29BxkrhhwwZSUguU9EnGZCZbkatUnEagkZSmAGJKR91cAUJlIInJYW_NAV6E5I7UlDTVSh0_UVR3wQn13mvOYttroVr-KoK2hRVNZp0Pd0tK6z0hi9pHGt985IYOyaDxOv47JfLvZr3fs5uy9Qx-OrfZnbJrCoO38kacZl7lIhRR_1DcYWEzU</recordid><startdate>20141001</startdate><enddate>20141001</enddate><creator>Chen, Xiaojun</creator><creator>Zhou, Weijun</creator><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20141001</creationdate><title>Convergence of the reweighted sub(1) minimization algorithm for sub(2)- sub( )pminimization</title><author>Chen, Xiaojun ; Zhou, Weijun</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_miscellaneous_16715836353</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Algorithms</topic><topic>Construction</topic><topic>Convergence</topic><topic>Image processing</topic><topic>Mathematical models</topic><topic>Minimization</topic><topic>Optimization</topic><topic>Signal reconstruction</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chen, Xiaojun</creatorcontrib><creatorcontrib>Zhou, Weijun</creatorcontrib><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Computational optimization and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chen, Xiaojun</au><au>Zhou, Weijun</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Convergence of the reweighted sub(1) minimization algorithm for sub(2)- sub( )pminimization</atitle><jtitle>Computational optimization and applications</jtitle><date>2014-10-01</date><risdate>2014</risdate><volume>59</volume><issue>1-2</issue><spage>47</spage><epage>61</epage><pages>47-61</pages><issn>0926-6003</issn><eissn>1573-2894</eissn><abstract>The iteratively reweighted sub(1) minimization algorithm (IRL1) has been widely used for variable selection, signal reconstruction and image processing. In this paper, we show that any sequence generated by the IRL1 is bounded and any accumulation point is a stationary point of the sub(2)- sub( )pminimization problem with 0&lt;p&lt;1. Moreover, the stationary point is a global minimizer and the convergence rate is approximately linear under certain conditions. We derive posteriori error bounds which can be used to construct practical stopping rules for the algorithm.</abstract><doi>10.1007/s10589-013-9553-8</doi></addata></record>
fulltext fulltext
identifier ISSN: 0926-6003
ispartof Computational optimization and applications, 2014-10, Vol.59 (1-2), p.47-61
issn 0926-6003
1573-2894
language eng
recordid cdi_proquest_miscellaneous_1671583635
source ABI/INFORM Collection; Business Source Ultimate【Trial: -2024/12/31】【Remote access available】; Springer Link
subjects Algorithms
Construction
Convergence
Image processing
Mathematical models
Minimization
Optimization
Signal reconstruction
title Convergence of the reweighted sub(1) minimization algorithm for sub(2)- sub( )pminimization
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-29T08%3A24%3A44IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Convergence%20of%20the%20reweighted%20sub(1)%20minimization%20algorithm%20for%20sub(2)-%20sub(%20)pminimization&rft.jtitle=Computational%20optimization%20and%20applications&rft.au=Chen,%20Xiaojun&rft.date=2014-10-01&rft.volume=59&rft.issue=1-2&rft.spage=47&rft.epage=61&rft.pages=47-61&rft.issn=0926-6003&rft.eissn=1573-2894&rft_id=info:doi/10.1007/s10589-013-9553-8&rft_dat=%3Cproquest%3E1671583635%3C/proquest%3E%3Cgrp_id%3Ecdi_FETCH-proquest_miscellaneous_16715836353%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=1671583635&rft_id=info:pmid/&rfr_iscdi=true