Convergence of a block coordinate descent method for nondifferentiable minimization
We study the convergence properties of a (block) coordinate descent method applied to minimize a nondifferentiable (nonconvex) function f(x1, . . . , xN) with certain separability and regularity properties. Assuming that f is continuous on a compact level set, the subsequence convergence of the iter...
Gespeichert in:
| Veröffentlicht in: | Journal of optimization theory and applications 2001-06, Vol.109 (3), p.475-494 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 494 |
|---|---|
| container_issue | 3 |
| container_start_page | 475 |
| container_title | Journal of optimization theory and applications |
| container_volume | 109 |
| creator | TSENG, P |
| description | We study the convergence properties of a (block) coordinate descent method applied to minimize a nondifferentiable (nonconvex) function f(x1, . . . , xN) with certain separability and regularity properties. Assuming that f is continuous on a compact level set, the subsequence convergence of the iterates to a stationary point is shown when either f is pseudoconvex in every pair of coordinate blocks from among N-1 coordinate blocks or f has at most one minimum in each of N-2 coordinate blocks. If f is quasiconvex and hemivariate in every coordinate block, then the assumptions of continuity of f and compactness of the level set may be relaxed further. These results are applied to derive new (and old) convergence results for the proximal minimization algorithm, an algorithm of Arimoto and Blahut, and an algorithm of Han. They are applied also to a problem of blind source separation. |
| doi_str_mv | 10.1023/a:1017501703105 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_743143283</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>743143283</sourcerecordid><originalsourceid>FETCH-LOGICAL-c439t-f2b626d243a72d0c2d40a1754e56a412c414d1cf277e4125237044ca1a810a2d3</originalsourceid><addsrcrecordid>eNpdUE1LAzEQDaJgrZ69BhE8rc3XbrbeSvELCh7Uc5jmQ1N3k5psBf31RtqDehiGGd578-YhdErJJSWMT-CKEirrUoRTUu-hEa0lr1gr2300IoSxijM-PURHOa8IIdNWihF6nMfwYdOLDdri6DDgZRf1G9YxJuMDDBYbm7UNA-7t8BoNdjHhEIPxztlU9h6WncW9D773XzD4GI7RgYMu25NdH6Pnm-un-V21eLi9n88WlRZ8OlSOLRvWGCY4SGaIZkYQKB8IWzcgKNOCCkO1Y1LaMtaMSyKEBgotJcAMH6OLre46xfeNzYPqfbHadRBs3GQlBaeCs5YX5Nk_5CpuUijmFJ02TUGV0MZosgXpFHNO1ql18j2kT0WJ-olYzdSfiAvjfCcLWUPnEgTt8y9aud3W_Bu7bnnb</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>196614370</pqid></control><display><type>article</type><title>Convergence of a block coordinate descent method for nondifferentiable minimization</title><source>SpringerNature Journals</source><creator>TSENG, P</creator><creatorcontrib>TSENG, P</creatorcontrib><description>We study the convergence properties of a (block) coordinate descent method applied to minimize a nondifferentiable (nonconvex) function f(x1, . . . , xN) with certain separability and regularity properties. Assuming that f is continuous on a compact level set, the subsequence convergence of the iterates to a stationary point is shown when either f is pseudoconvex in every pair of coordinate blocks from among N-1 coordinate blocks or f has at most one minimum in each of N-2 coordinate blocks. If f is quasiconvex and hemivariate in every coordinate block, then the assumptions of continuity of f and compactness of the level set may be relaxed further. These results are applied to derive new (and old) convergence results for the proximal minimization algorithm, an algorithm of Arimoto and Blahut, and an algorithm of Han. They are applied also to a problem of blind source separation.</description><identifier>ISSN: 0022-3239</identifier><identifier>EISSN: 1573-2878</identifier><identifier>DOI: 10.1023/a:1017501703105</identifier><identifier>CODEN: JOTABN</identifier><language>eng</language><publisher>New York, NY: Springer</publisher><subject>Algorithms ; Applied sciences ; Exact sciences and technology ; Operational research and scientific management ; Operational research. Management science ; Optimization. Search problems</subject><ispartof>Journal of optimization theory and applications, 2001-06, Vol.109 (3), p.475-494</ispartof><rights>2001 INIST-CNRS</rights><rights>Plenum Publishing Corporation 2001</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c439t-f2b626d243a72d0c2d40a1754e56a412c414d1cf277e4125237044ca1a810a2d3</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=1028385$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>TSENG, P</creatorcontrib><title>Convergence of a block coordinate descent method for nondifferentiable minimization</title><title>Journal of optimization theory and applications</title><description>We study the convergence properties of a (block) coordinate descent method applied to minimize a nondifferentiable (nonconvex) function f(x1, . . . , xN) with certain separability and regularity properties. Assuming that f is continuous on a compact level set, the subsequence convergence of the iterates to a stationary point is shown when either f is pseudoconvex in every pair of coordinate blocks from among N-1 coordinate blocks or f has at most one minimum in each of N-2 coordinate blocks. If f is quasiconvex and hemivariate in every coordinate block, then the assumptions of continuity of f and compactness of the level set may be relaxed further. These results are applied to derive new (and old) convergence results for the proximal minimization algorithm, an algorithm of Arimoto and Blahut, and an algorithm of Han. They are applied also to a problem of blind source separation.</description><subject>Algorithms</subject><subject>Applied sciences</subject><subject>Exact sciences and technology</subject><subject>Operational research and scientific management</subject><subject>Operational research. Management science</subject><subject>Optimization. Search problems</subject><issn>0022-3239</issn><issn>1573-2878</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2001</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNpdUE1LAzEQDaJgrZ69BhE8rc3XbrbeSvELCh7Uc5jmQ1N3k5psBf31RtqDehiGGd578-YhdErJJSWMT-CKEirrUoRTUu-hEa0lr1gr2300IoSxijM-PURHOa8IIdNWihF6nMfwYdOLDdri6DDgZRf1G9YxJuMDDBYbm7UNA-7t8BoNdjHhEIPxztlU9h6WncW9D773XzD4GI7RgYMu25NdH6Pnm-un-V21eLi9n88WlRZ8OlSOLRvWGCY4SGaIZkYQKB8IWzcgKNOCCkO1Y1LaMtaMSyKEBgotJcAMH6OLre46xfeNzYPqfbHadRBs3GQlBaeCs5YX5Nk_5CpuUijmFJ02TUGV0MZosgXpFHNO1ql18j2kT0WJ-olYzdSfiAvjfCcLWUPnEgTt8y9aud3W_Bu7bnnb</recordid><startdate>20010601</startdate><enddate>20010601</enddate><creator>TSENG, P</creator><general>Springer</general><general>Springer Nature B.V</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KR7</scope><scope>L.-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20010601</creationdate><title>Convergence of a block coordinate descent method for nondifferentiable minimization</title><author>TSENG, P</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c439t-f2b626d243a72d0c2d40a1754e56a412c414d1cf277e4125237044ca1a810a2d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2001</creationdate><topic>Algorithms</topic><topic>Applied sciences</topic><topic>Exact sciences and technology</topic><topic>Operational research and scientific management</topic><topic>Operational research. Management science</topic><topic>Optimization. Search problems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>TSENG, P</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Access via ABI/INFORM (ProQuest)</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering 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><collection>ABI/INFORM Global</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Journal of optimization theory and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>TSENG, P</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Convergence of a block coordinate descent method for nondifferentiable minimization</atitle><jtitle>Journal of optimization theory and applications</jtitle><date>2001-06-01</date><risdate>2001</risdate><volume>109</volume><issue>3</issue><spage>475</spage><epage>494</epage><pages>475-494</pages><issn>0022-3239</issn><eissn>1573-2878</eissn><coden>JOTABN</coden><abstract>We study the convergence properties of a (block) coordinate descent method applied to minimize a nondifferentiable (nonconvex) function f(x1, . . . , xN) with certain separability and regularity properties. Assuming that f is continuous on a compact level set, the subsequence convergence of the iterates to a stationary point is shown when either f is pseudoconvex in every pair of coordinate blocks from among N-1 coordinate blocks or f has at most one minimum in each of N-2 coordinate blocks. If f is quasiconvex and hemivariate in every coordinate block, then the assumptions of continuity of f and compactness of the level set may be relaxed further. These results are applied to derive new (and old) convergence results for the proximal minimization algorithm, an algorithm of Arimoto and Blahut, and an algorithm of Han. They are applied also to a problem of blind source separation.</abstract><cop>New York, NY</cop><pub>Springer</pub><doi>10.1023/a:1017501703105</doi><tpages>20</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0022-3239 |
| ispartof | Journal of optimization theory and applications, 2001-06, Vol.109 (3), p.475-494 |
| issn | 0022-3239 1573-2878 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_743143283 |
| source | SpringerNature Journals |
| subjects | Algorithms Applied sciences Exact sciences and technology Operational research and scientific management Operational research. Management science Optimization. Search problems |
| title | Convergence of a block coordinate descent method for nondifferentiable minimization |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-19T20%3A11%3A11IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Convergence%20of%20a%20block%20coordinate%20descent%20method%20for%20nondifferentiable%20minimization&rft.jtitle=Journal%20of%20optimization%20theory%20and%20applications&rft.au=TSENG,%20P&rft.date=2001-06-01&rft.volume=109&rft.issue=3&rft.spage=475&rft.epage=494&rft.pages=475-494&rft.issn=0022-3239&rft.eissn=1573-2878&rft.coden=JOTABN&rft_id=info:doi/10.1023/a:1017501703105&rft_dat=%3Cproquest_cross%3E743143283%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=196614370&rft_id=info:pmid/&rfr_iscdi=true |