{"id":"https://openalex.org/W3038810201","doi":"https://doi.org/10.1137/19m1270987","title":"Several Classes of Stationary Points for Rank Regularized Minimization Problems","display_name":"Several Classes of Stationary Points for Rank Regularized Minimization Problems","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3038810201","doi":"https://doi.org/10.1137/19m1270987","mag":"3038810201"},"language":"en","primary_location":{"id":"doi:10.1137/19m1270987","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1270987","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","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/A5100768696","display_name":"Yulan Liu","orcid":"https://orcid.org/0000-0001-7253-3365"},"institutions":[{"id":"https://openalex.org/I139024713","display_name":"Guangdong University of Technology","ror":"https://ror.org/04azbjn80","country_code":"CN","type":"education","lineage":["https://openalex.org/I139024713"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yulan Liu","raw_affiliation_strings":["School of Applied Mathematics, Guangdong University of Technology, Guangzhou"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Applied Mathematics, Guangdong University of Technology, Guangzhou","institution_ids":["https://openalex.org/I139024713"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086425260","display_name":"Shujun Bi","orcid":"https://orcid.org/0000-0002-4215-2729"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shujun Bi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5090153413","display_name":"Shaohua Pan","orcid":"https://orcid.org/0000-0002-6261-5268"},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shaohua Pan","raw_affiliation_strings":["School of Mathematics, South China University of Technology, Guangzhou"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, South China University of Technology, Guangzhou","institution_ids":["https://openalex.org/I90610280"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090153413"],"corresponding_institution_ids":["https://openalex.org/I90610280"],"apc_list":null,"apc_paid":null,"fwci":0.8217,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.68761456,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"30","issue":"2","first_page":"1756","last_page":"1775"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"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":0.9995999932289124,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9987000226974487,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9843000173568726,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8394396901130676},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.7853593826293945},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7143023610115051},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.645607054233551},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.5874131917953491},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5561689138412476},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5422069430351257},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.46648433804512024},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3853060007095337},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.17796093225479126},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0654776394367218}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8394396901130676},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7853593826293945},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7143023610115051},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.645607054233551},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.5874131917953491},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5561689138412476},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5422069430351257},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.46648433804512024},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3853060007095337},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.17796093225479126},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0654776394367218},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1270987","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1270987","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.8100000023841858}],"awards":[{"id":"https://openalex.org/G3095804135","display_name":"\u7ed3\u6784\u4f4e\u79e9\u77e9\u9635\u4f18\u5316\u95ee\u9898\u7684\u591a\u9636\u6bb5\u51f8\u677e\u5f1b\u6cd5\u7814\u7a76","funder_award_id":"11571120","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3132854653","display_name":"\u4f4e\u79e9\u77e9\u9635\u4f18\u5316\u95ee\u9898\u7684\u7a33\u5b9a\u6027\u7814\u7a76\u53ca\u7b97\u6cd5\u4e2d\u7684\u5e94\u7528","funder_award_id":"11971177","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6927871888","display_name":null,"funder_award_id":"11701186","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W638016179","https://openalex.org/W1235853611","https://openalex.org/W1997605385","https://openalex.org/W1998913007","https://openalex.org/W2010337082","https://openalex.org/W2029213856","https://openalex.org/W2030451378","https://openalex.org/W2031906930","https://openalex.org/W2033155834","https://openalex.org/W2056145308","https://openalex.org/W2077161157","https://openalex.org/W2096220424","https://openalex.org/W2150140216","https://openalex.org/W2166163936","https://openalex.org/W2171587393","https://openalex.org/W2225235077","https://openalex.org/W2268674159","https://openalex.org/W2586353914","https://openalex.org/W2598746244","https://openalex.org/W2610303444","https://openalex.org/W2745004303","https://openalex.org/W2756157737","https://openalex.org/W2962771824","https://openalex.org/W2964192982","https://openalex.org/W3023814688"],"related_works":["https://openalex.org/W2152992791","https://openalex.org/W2112835755","https://openalex.org/W2807251790","https://openalex.org/W2349674371","https://openalex.org/W4291951920","https://openalex.org/W2097495471","https://openalex.org/W1696545756","https://openalex.org/W4301867002","https://openalex.org/W2952827811","https://openalex.org/W2056202066"],"abstract_inverted_index":{"For":[0],"the":[1,14,22,30,35,38,44,48],"rank":[2],"regularized":[3],"minimization":[4],"problem,":[5],"we":[6],"introduce":[7],"several":[8],"classes":[9],"of":[10,34,47,78],"stationary":[11,60],"points":[12],"by":[13,42],"problem":[15],"itself":[16],"and":[17,37],"its":[18],"equivalent":[19],"reformulations":[20],"including":[21],"mathematical":[23],"program":[24],"with":[25],"an":[26,67],"equilibrium":[27],"constraint":[28],"(MPEC),":[29],"global":[31,49],"exact":[32,50],"penalty":[33],"MPEC,":[36],"difference-of-convex":[39],"surrogate":[40],"yielded":[41],"eliminating":[43],"dual":[45],"part":[46],"penalty.":[51],"A":[52],"clear":[53],"relation":[54],"chart":[55],"is":[56],"established":[57],"among":[58],"these":[59],"points,":[61],"which":[62],"offers":[63],"guidance":[64],"to":[65,75],"choose":[66],"appropriate":[68],"reformulation":[69],"for":[70],"seeking":[71],"a":[72],"low-rank":[73],"solution":[74],"this":[76],"class":[77],"problems.":[79]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":3}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}