{"id":"https://openalex.org/W2523528550","doi":"https://doi.org/10.1137/141002220","title":"Modulus-Type Inner Outer Iteration Methods for Nonnegative Constrained Least Squares Problems","display_name":"Modulus-Type Inner Outer Iteration Methods for Nonnegative Constrained Least Squares Problems","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2523528550","doi":"https://doi.org/10.1137/141002220","mag":"2523528550"},"language":"en","primary_location":{"id":"doi:10.1137/141002220","is_oa":false,"landing_page_url":"https://doi.org/10.1137/141002220","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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/A5066804442","display_name":"Ning Zheng","orcid":"https://orcid.org/0000-0002-0451-6536"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ning Zheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072176609","display_name":"Ken Hayami","orcid":"https://orcid.org/0000-0001-9640-586X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ken Hayami","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108133091","display_name":"Jun-Feng Yin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jun-Feng Yin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6135,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.90804598,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"37","issue":"3","first_page":"1250","last_page":"1278"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9988999962806702,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9968000054359436,"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/mathematics","display_name":"Mathematics","score":0.8226110935211182},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.624045193195343},{"id":"https://openalex.org/keywords/linear-least-squares","display_name":"Linear least squares","score":0.6181532740592957},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5861733555793762},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5176523327827454},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5139222145080566},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45006006956100464},{"id":"https://openalex.org/keywords/complementarity","display_name":"Complementarity (molecular biology)","score":0.4488636255264282},{"id":"https://openalex.org/keywords/non-linear-least-squares","display_name":"Non-linear least squares","score":0.44454288482666016},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4243488609790802},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.09814059734344482},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0857526957988739}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8226110935211182},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.624045193195343},{"id":"https://openalex.org/C58663186","wikidata":"https://www.wikidata.org/wiki/Q6553462","display_name":"Linear least squares","level":3,"score":0.6181532740592957},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5861733555793762},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5176523327827454},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5139222145080566},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45006006956100464},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.4488636255264282},{"id":"https://openalex.org/C45923927","wikidata":"https://www.wikidata.org/wiki/Q3319230","display_name":"Non-linear least squares","level":3,"score":0.44454288482666016},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4243488609790802},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.09814059734344482},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0857526957988739},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/141002220","is_oa":false,"landing_page_url":"https://doi.org/10.1137/141002220","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2713586455","display_name":"The fast solution of least squares problems and its applications.","funder_award_id":"15K04768","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G7402170985","display_name":"\u98ce\u9669\u7ba1\u7406\u4e2d\u671f\u6743\u5b9a\u4ef7\u6a21\u578b\u7684\u82e5\u5e72\u9ad8\u6548\u6570\u503c\u65b9\u6cd5\u7814\u7a76","funder_award_id":"11271289","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1981648990","https://openalex.org/W1982337446","https://openalex.org/W1989387477","https://openalex.org/W2002102128","https://openalex.org/W2014851363","https://openalex.org/W2016278506","https://openalex.org/W2020584829","https://openalex.org/W2026289804","https://openalex.org/W2030123043","https://openalex.org/W2033242948","https://openalex.org/W2048721028","https://openalex.org/W2054786539","https://openalex.org/W2054967989","https://openalex.org/W2056950638","https://openalex.org/W2069053817","https://openalex.org/W2081659125","https://openalex.org/W2083229815","https://openalex.org/W2084123115","https://openalex.org/W2088078069","https://openalex.org/W2089529944","https://openalex.org/W2094357863","https://openalex.org/W2098132613","https://openalex.org/W2116147316","https://openalex.org/W2132347401"],"related_works":["https://openalex.org/W2026673180","https://openalex.org/W2030255580","https://openalex.org/W4380487384","https://openalex.org/W1959514624","https://openalex.org/W327962130","https://openalex.org/W4378552425","https://openalex.org/W2027973524","https://openalex.org/W1911118692","https://openalex.org/W200101083","https://openalex.org/W2034819163"],"abstract_inverted_index":{"For":[0],"the":[1,21,25,29,34,39,45,49,56,60,66,71,79,87,96,100,104,112,117,120,126,129],"solution":[2,118],"of":[3,48,59,91,128],"large":[4],"sparse":[5],"nonnegative":[6,121],"constrained":[7],"linear":[8,40],"least":[9,107],"squares":[10,108],"(NNLS)":[11],"problems,":[12],"a":[13],"new":[14],"iterative":[15,31],"method":[16,23,32,72],"is":[17,63],"proposed":[18,67,130],"which":[19,83],"uses":[20],"CGLS":[22],"for":[24,33,65],"inner":[26],"iterations":[27,36,93],"and":[28,115,141],"modulus":[30,92],"outer":[35],"to":[37,94,133],"solve":[38],"complementarity":[41],"problem":[42],"resulting":[43],"from":[44],"Karush--Kuhn--Tucker":[46],"conditions":[47],"NNLS":[50],"problem.":[51],"Theoretical":[52],"convergence":[53],"analysis":[54],"including":[55],"optimal":[57],"choice":[58],"parameter":[61],"matrix":[62],"presented":[64],"method.":[68],"In":[69],"addition,":[70],"can":[73],"be":[74],"further":[75],"enhanced":[76],"by":[77],"incorporating":[78],"active":[80,97],"set":[81],"strategy,":[82],"contains":[84],"two":[85],"stages;":[86],"first":[88],"stage":[89,102],"consists":[90],"identify":[95],"set,":[98],"while":[99],"second":[101],"solves":[103],"reduced":[105],"unconstrained":[106],"problems":[109],"only":[110],"on":[111],"inactive":[113],"variables,":[114],"projects":[116],"into":[119],"region.":[122],"Numerical":[123],"experiments":[124],"show":[125],"efficiency":[127],"methods":[131,136],"compared":[132],"projection":[134],"gradient--type":[135],"with":[137],"fewer":[138],"iteration":[139],"steps":[140],"less":[142],"CPU":[143],"time.":[144]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-12T07:12:00.856984","created_date":"2025-10-10T00:00:00"}
