{"id":"https://openalex.org/W1968154520","doi":"https://doi.org/10.1137/120887795","title":"A Block Coordinate Descent Method for Regularized Multiconvex Optimization with Applications to Nonnegative Tensor Factorization and Completion","display_name":"A Block Coordinate Descent Method for Regularized Multiconvex Optimization with Applications to Nonnegative Tensor Factorization and Completion","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1968154520","doi":"https://doi.org/10.1137/120887795","mag":"1968154520"},"language":"en","primary_location":{"id":"doi:10.1137/120887795","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120887795","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055895298","display_name":"Yangyang Xu","orcid":"https://orcid.org/0000-0002-4163-3723"},"institutions":[{"id":"https://openalex.org/I4210107842","display_name":"Institute of Mathematics and its Applications","ror":"https://ror.org/01rxg5p40","country_code":"GB","type":"education","lineage":["https://openalex.org/I4210107842"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Yangyang Xu","raw_affiliation_strings":["Institute for Mathematics and its Applications"],"affiliations":[{"raw_affiliation_string":"Institute for Mathematics and its Applications","institution_ids":["https://openalex.org/I4210107842"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085908411","display_name":"Wotao Yin","orcid":"https://orcid.org/0000-0001-6697-9731"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wotao Yin","raw_affiliation_strings":["**Rice University;"],"affiliations":[{"raw_affiliation_string":"**Rice University;","institution_ids":["https://openalex.org/I74775410"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5055895298"],"corresponding_institution_ids":["https://openalex.org/I4210107842"],"apc_list":null,"apc_paid":null,"fwci":64.4837,"has_fulltext":false,"cited_by_count":1199,"citation_normalized_percentile":{"value":0.99973016,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"6","issue":"3","first_page":"1758","last_page":"1789"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/coordinate-descent","display_name":"Coordinate descent","score":0.817475438117981},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.5179120898246765},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5166197419166565},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4932500720024109},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.4926460385322571},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.49253806471824646},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.48972299695014954},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4781404733657837},{"id":"https://openalex.org/keywords/non-negative-matrix-factorization","display_name":"Non-negative matrix factorization","score":0.4764010012149811},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4472372531890869},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4380559027194977},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41609951853752136},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4114747941493988},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34282779693603516},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.24448752403259277},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11830607056617737}],"concepts":[{"id":"https://openalex.org/C157553263","wikidata":"https://www.wikidata.org/wiki/Q5168004","display_name":"Coordinate descent","level":2,"score":0.817475438117981},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.5179120898246765},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5166197419166565},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4932500720024109},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.4926460385322571},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49253806471824646},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.48972299695014954},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4781404733657837},{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.4764010012149811},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4472372531890869},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4380559027194977},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41609951853752136},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4114747941493988},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34282779693603516},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.24448752403259277},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11830607056617737},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/120887795","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120887795","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5699999928474426,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":80,"referenced_works":["https://openalex.org/W17407774","https://openalex.org/W206759535","https://openalex.org/W654824284","https://openalex.org/W1485161427","https://openalex.org/W1531121930","https://openalex.org/W1539838732","https://openalex.org/W1540764732","https://openalex.org/W1561391377","https://openalex.org/W1846534543","https://openalex.org/W1902027874","https://openalex.org/W1963826206","https://openalex.org/W1976391658","https://openalex.org/W1979089199","https://openalex.org/W1982079894","https://openalex.org/W1986326495","https://openalex.org/W1986594951","https://openalex.org/W1996355918","https://openalex.org/W2005876975","https://openalex.org/W2007449884","https://openalex.org/W2010364595","https://openalex.org/W2013029404","https://openalex.org/W2016425264","https://openalex.org/W2017288758","https://openalex.org/W2017966952","https://openalex.org/W2021361347","https://openalex.org/W2021989611","https://openalex.org/W2022164193","https://openalex.org/W2022393739","https://openalex.org/W2022541060","https://openalex.org/W2024165284","https://openalex.org/W2026034143","https://openalex.org/W2038237443","https://openalex.org/W2038497950","https://openalex.org/W2038647687","https://openalex.org/W2039050532","https://openalex.org/W2041326514","https://openalex.org/W2041815422","https://openalex.org/W2050968963","https://openalex.org/W2059745395","https://openalex.org/W2069213542","https://openalex.org/W2073502026","https://openalex.org/W2076566842","https://openalex.org/W2078204800","https://openalex.org/W2078853581","https://openalex.org/W2079277602","https://openalex.org/W2082639035","https://openalex.org/W2084978503","https://openalex.org/W2090963365","https://openalex.org/W2091449379","https://openalex.org/W2093417350","https://openalex.org/W2100556411","https://openalex.org/W2108138101","https://openalex.org/W2108837778","https://openalex.org/W2110096996","https://openalex.org/W2110509222","https://openalex.org/W2113606819","https://openalex.org/W2117852776","https://openalex.org/W2118550318","https://openalex.org/W2118718620","https://openalex.org/W2120816706","https://openalex.org/W2129732816","https://openalex.org/W2129753219","https://openalex.org/W2133069808","https://openalex.org/W2133459316","https://openalex.org/W2135029798","https://openalex.org/W2135046866","https://openalex.org/W2136127419","https://openalex.org/W2136171036","https://openalex.org/W2138019504","https://openalex.org/W2140318696","https://openalex.org/W2143030432","https://openalex.org/W2144920235","https://openalex.org/W2160547390","https://openalex.org/W2161219071","https://openalex.org/W2331639718","https://openalex.org/W2620898487","https://openalex.org/W2901918405","https://openalex.org/W3101457173","https://openalex.org/W3142300713","https://openalex.org/W3143596294"],"related_works":["https://openalex.org/W2127243424","https://openalex.org/W4390394189","https://openalex.org/W2037504162","https://openalex.org/W2539013788","https://openalex.org/W2792706544","https://openalex.org/W1568451138","https://openalex.org/W2156699640","https://openalex.org/W2045265907","https://openalex.org/W2972997031","https://openalex.org/W34555840"],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"regularized":[3],"block":[4,21,48],"multiconvex":[5],"optimization,":[6],"where":[7],"the":[8,62,73,78,86,124,131,135,164],"feasible":[9],"set":[10],"and":[11,29,44,71,97,104,115,126,144,154],"objective":[12],"function":[13],"are":[14,92,161],"generally":[15],"nonconvex":[16,27],"but":[17],"convex":[18],"in":[19,141],"each":[20],"of":[22,77,150],"variables.":[23],"It":[24],"also":[25],"accepts":[26],"blocks":[28,32],"requires":[30],"these":[31],"to":[33,130],"be":[34],"updated":[35],"by":[36,80],"proximal":[37],"minimization.":[38],"We":[39],"review":[40],"some":[41],"interesting":[42],"applications":[43],"propose":[45],"a":[46,82,158],"generalized":[47],"coordinate":[49],"descent":[50],"method.":[51],"Under":[52],"certain":[53],"conditions,":[54],"we":[55,67],"show":[56],"that":[57],"any":[58],"limit":[59],"point":[60],"satisfies":[61],"Nash":[63],"equilibrium":[64],"conditions.":[65],"Furthermore,":[66],"establish":[68],"global":[69],"convergence":[70,75],"estimate":[72],"asymptotic":[74],"rate":[76],"method":[79],"assuming":[81],"property":[83],"based":[84],"on":[85,94],"Kurdyka--\u0141ojasiewicz":[87],"inequality.":[88],"The":[89,110,147],"proposed":[90,136],"algorithms":[91,137],"tested":[93],"nonnegative":[95,151],"matrix":[96,103],"tensor":[98,105],"factorization,":[99],"as":[100,102,118,120],"well":[101,119],"recovery":[106],"from":[107,123,163],"incomplete":[108],"observations.":[109],"tests":[111],"include":[112],"synthetic":[113],"data":[114],"hyperspectral":[116],"data,":[117],"image":[121],"sets":[122],"CBCL":[125],"ORL":[127],"databases.":[128],"Compared":[129],"existing":[132],"state-of-the-art":[133],"algorithms,":[134],"demonstrate":[138],"superior":[139],"performance":[140],"both":[142],"speed":[143],"solution":[145],"quality.":[146],"MATLAB":[148],"code":[149],"matrix/tensor":[152],"decomposition":[153],"completion,":[155],"along":[156],"with":[157],"few":[159],"demos,":[160],"accessible":[162],"authors'":[165],"homepages.":[166]},"counts_by_year":[{"year":2026,"cited_by_count":26},{"year":2025,"cited_by_count":70},{"year":2024,"cited_by_count":93},{"year":2023,"cited_by_count":85},{"year":2022,"cited_by_count":103},{"year":2021,"cited_by_count":137},{"year":2020,"cited_by_count":134},{"year":2019,"cited_by_count":150},{"year":2018,"cited_by_count":118},{"year":2017,"cited_by_count":100},{"year":2016,"cited_by_count":74},{"year":2015,"cited_by_count":64},{"year":2014,"cited_by_count":34},{"year":2013,"cited_by_count":11}],"updated_date":"2026-04-11T08:14:18.477133","created_date":"2025-10-10T00:00:00"}