{"id":"https://openalex.org/W2910761930","doi":"https://doi.org/10.1109/tnnls.2018.2885699","title":"Scalable Proximal Jacobian Iteration Method With Global Convergence Analysis for Nonconvex Unconstrained Composite Optimizations","display_name":"Scalable Proximal Jacobian Iteration Method With Global Convergence Analysis for Nonconvex Unconstrained Composite Optimizations","publication_year":2019,"publication_date":"2019-01-15","ids":{"openalex":"https://openalex.org/W2910761930","doi":"https://doi.org/10.1109/tnnls.2018.2885699","mag":"2910761930","pmid":"https://pubmed.ncbi.nlm.nih.gov/30668503"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2018.2885699","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2018.2885699","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5066566618","display_name":"Hengmin Zhang","orcid":"https://orcid.org/0000-0002-2472-6637"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hengmin Zhang","raw_affiliation_strings":["PCA Lab, Key Laboratory of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, Nanjing University of Science and Technology, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-2472-6637","affiliations":[{"raw_affiliation_string":"PCA Lab, Key Laboratory of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, Nanjing University of Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I36399199"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064363522","display_name":"Jianjun Qian","orcid":"https://orcid.org/0000-0002-0968-8556"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianjun Qian","raw_affiliation_strings":["PCA Lab, Key Laboratory of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, Nanjing University of Science and Technology, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-0968-8556","affiliations":[{"raw_affiliation_string":"PCA Lab, Key Laboratory of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, Nanjing University of Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I36399199"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015817857","display_name":"Junbin Gao","orcid":"https://orcid.org/0000-0001-9803-0256"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Junbin Gao","raw_affiliation_strings":["Discipline of Business Analytics, The University of Sydney Business School, The University of Sydney, Sydney, NSW, Australia"],"raw_orcid":"https://orcid.org/0000-0001-9803-0256","affiliations":[{"raw_affiliation_string":"Discipline of Business Analytics, The University of Sydney Business School, The University of Sydney, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100726984","display_name":"Jian Yang","orcid":"https://orcid.org/0000-0003-4800-832X"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Yang","raw_affiliation_strings":["Jiangsu Key Laboratory of Image and Video Understanding for Social Security School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0003-4800-832X","affiliations":[{"raw_affiliation_string":"Jiangsu Key Laboratory of Image and Video Understanding for Social Security School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I36399199"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054364063","display_name":"Chunyan Xu","orcid":"https://orcid.org/0000-0002-0814-4362"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chunyan Xu","raw_affiliation_strings":["Jiangsu Key Laboratory of Image and Video Understanding for Social Security School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-0814-4362","affiliations":[{"raw_affiliation_string":"Jiangsu Key Laboratory of Image and Video Understanding for Social Security School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I36399199"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.0968,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.94106464,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"30","issue":"9","first_page":"2825","last_page":"2839"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9997000098228455,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9991999864578247,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9950000047683716,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.7806427478790283},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7522853016853333},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.6645622253417969},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5617673397064209},{"id":"https://openalex.org/keywords/composite-number","display_name":"Composite number","score":0.5234367847442627},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4985215663909912},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4942353069782257},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4154036343097687},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34895169734954834}],"concepts":[{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.7806427478790283},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7522853016853333},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.6645622253417969},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5617673397064209},{"id":"https://openalex.org/C104779481","wikidata":"https://www.wikidata.org/wiki/Q50707","display_name":"Composite number","level":2,"score":0.5234367847442627},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4985215663909912},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4942353069782257},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4154036343097687},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34895169734954834},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2018.2885699","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2018.2885699","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:30668503","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/30668503","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4776286764","display_name":null,"funder_award_id":"30918011321","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G8684234662","display_name":null,"funder_award_id":"2014CB349303","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320321883","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":98,"referenced_works":["https://openalex.org/W74424801","https://openalex.org/W195665135","https://openalex.org/W1482071412","https://openalex.org/W1486694121","https://openalex.org/W1507780841","https://openalex.org/W1551360398","https://openalex.org/W1586424387","https://openalex.org/W1600550542","https://openalex.org/W1736339626","https://openalex.org/W1860736741","https://openalex.org/W1906374873","https://openalex.org/W1923817890","https://openalex.org/W1943431218","https://openalex.org/W1965125844","https://openalex.org/W1967138577","https://openalex.org/W1969698720","https://openalex.org/W1992841740","https://openalex.org/W1993962865","https://openalex.org/W1997201895","https://openalex.org/W2021361347","https://openalex.org/W2022541060","https://openalex.org/W2023271934","https://openalex.org/W2025666718","https://openalex.org/W2027982384","https://openalex.org/W2045079045","https://openalex.org/W2045983409","https://openalex.org/W2047071281","https://openalex.org/W2057624533","https://openalex.org/W2058532290","https://openalex.org/W2059639989","https://openalex.org/W2071631699","https://openalex.org/W2074682976","https://openalex.org/W2078853581","https://openalex.org/W2079775628","https://openalex.org/W2084983808","https://openalex.org/W2100556411","https://openalex.org/W2103972604","https://openalex.org/W2107861471","https://openalex.org/W2110531331","https://openalex.org/W2111854674","https://openalex.org/W2118550318","https://openalex.org/W2129732816","https://openalex.org/W2129812935","https://openalex.org/W2131628350","https://openalex.org/W2142224912","https://openalex.org/W2145962650","https://openalex.org/W2150489380","https://openalex.org/W2154231875","https://openalex.org/W2158121106","https://openalex.org/W2164278908","https://openalex.org/W2166956514","https://openalex.org/W2184634347","https://openalex.org/W2187214659","https://openalex.org/W2216139520","https://openalex.org/W2233977894","https://openalex.org/W2288624927","https://openalex.org/W2295652899","https://openalex.org/W2338953098","https://openalex.org/W2339666411","https://openalex.org/W2343516804","https://openalex.org/W2401764675","https://openalex.org/W2471758726","https://openalex.org/W2502891885","https://openalex.org/W2505029951","https://openalex.org/W2507294395","https://openalex.org/W2571537824","https://openalex.org/W2572018699","https://openalex.org/W2588939073","https://openalex.org/W2606011186","https://openalex.org/W2626376214","https://openalex.org/W2747056667","https://openalex.org/W2752077201","https://openalex.org/W2768166594","https://openalex.org/W2791026767","https://openalex.org/W2936995161","https://openalex.org/W2963218026","https://openalex.org/W2963664109","https://openalex.org/W2963965423","https://openalex.org/W2964011556","https://openalex.org/W3098306969","https://openalex.org/W3100203369","https://openalex.org/W3102415113","https://openalex.org/W3141595720","https://openalex.org/W3199556078","https://openalex.org/W4249513058","https://openalex.org/W4292363360","https://openalex.org/W6603014808","https://openalex.org/W6607912541","https://openalex.org/W6628883312","https://openalex.org/W6679973066","https://openalex.org/W6682205712","https://openalex.org/W6682433143","https://openalex.org/W6684416548","https://openalex.org/W6686534882","https://openalex.org/W6695971140","https://openalex.org/W6724489458","https://openalex.org/W6731676268","https://openalex.org/W6761030284"],"related_works":["https://openalex.org/W2007405763","https://openalex.org/W3136087161","https://openalex.org/W1486373823","https://openalex.org/W2119578520","https://openalex.org/W2053762185","https://openalex.org/W2913611334","https://openalex.org/W1984283682","https://openalex.org/W1965257389","https://openalex.org/W2018238589","https://openalex.org/W2145980196"],"abstract_inverted_index":{"-norm":[0],"and":[1,49,116,166,187],"rank":[2],"function":[3],"minimization":[4],"problems.":[5],"However,":[6],"due":[7],"to":[8,70,120,135,144,183],"the":[9,28,33,50,57,68,71,93,99,105,111,122,138,150,164,171,176,180,184,197],"absence":[10],"of":[11,31,38,82,101,108,158,170],"convexity":[12],"in":[13,133,175],"these":[14],"nonconvex":[15,83,185],"problems,":[16,190],"developing":[17],"efficient":[18],"algorithms":[19,200],"with":[20,46,60,79,87],"convergence":[21,131,168,205],"guarantee":[22],"becomes":[23],"very":[24],"challenging.":[25],"Inspired":[26],"by":[27,97,148],"basic":[29],"ideas":[30],"both":[32,119],"Jacobian":[34,73],"alternating":[35],"direction":[36],"method":[37],"multipliers":[39],"(JADMMs)":[40],"for":[41,55,77,154],"solving":[42],"linearly":[43],"constrained":[44],"problems":[45,59,86],"separable":[47],"objectives":[48],"proximal":[51,72],"gradient":[52],"methods":[53,75],"(PGMs)":[54],"optimizing":[56],"unconstrained":[58],"one":[61],"variable,":[62],"this":[63],"paper":[64],"focuses":[65],"on":[66],"extending":[67],"PGMs":[69],"iteration":[74],"(PJIMs)":[76],"handling":[78],"a":[80,129,145,155],"family":[81],"composite":[84],"optimization":[85],"two":[88],"splitting":[89],"variables.":[90],"To":[91],"reduce":[92],"total":[94],"computational":[95],"complexity":[96],"decreasing":[98],"number":[100],"iterations,":[102],"we":[103,127,161],"devise":[104],"accelerated":[106],"version":[107],"PJIMs":[109],"through":[110],"well-known":[112],"Nesterov's":[113],"acceleration":[114],"strategy":[115],"further":[117],"extend":[118],"solve":[121],"multivariable":[123],"cases.":[124],"Most":[125],"importantly,":[126],"provide":[128],"rigorous":[130],"analysis,":[132],"theory,":[134],"show":[136],"that":[137,196],"generated":[139],"variable":[140,173],"sequence":[141,174],"globally":[142],"converges":[143],"critical":[146],"point":[147],"exploiting":[149],"Kurdyka-\u0141ojasiewica":[151],"(K\u0141)":[152],"property":[153],"broad":[156],"class":[157],"functions.":[159],"Furthermore,":[160],"also":[162,208],"establish":[163],"linear":[165],"sublinear":[167],"rates":[169],"obtained":[172],"objective":[177],"function.":[178],"As":[179],"specific":[181],"application":[182],"sparse":[186],"low-rank":[188],"recovery":[189],"several":[191],"numerical":[192],"experiments":[193],"can":[194],"verify":[195],"newly":[198],"proposed":[199],"not":[201],"only":[202],"keep":[203],"fast":[204],"speed":[206],"but":[207],"have":[209],"high":[210],"precision.":[211]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
