{"id":"https://openalex.org/W4376129296","doi":"https://doi.org/10.1137/22m1476733","title":"Finding the Least Element of a Nonnegative Solution Set of a Class of Polynomial Inequalities","display_name":"Finding the Least Element of a Nonnegative Solution Set of a Class of Polynomial Inequalities","publication_year":2023,"publication_date":"2023-05-11","ids":{"openalex":"https://openalex.org/W4376129296","doi":"https://doi.org/10.1137/22m1476733"},"language":"en","primary_location":{"id":"doi:10.1137/22m1476733","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1476733","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/A5050088762","display_name":"Zheng\u2010Hai Huang","orcid":"https://orcid.org/0000-0003-2269-961X"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zheng-Hai Huang","raw_affiliation_strings":["School of Mathematics, Tianjin University, Tianjin 300354, People\u2019s Republic of China","School of Mathematics, Tianjin University, Tianjin 300354, People's Republic of China"],"raw_orcid":"https://orcid.org/0000-0003-2269-961X","affiliations":[{"raw_affiliation_string":"School of Mathematics, Tianjin University, Tianjin 300354, People\u2019s Republic of China","institution_ids":["https://openalex.org/I162868743"]},{"raw_affiliation_string":"School of Mathematics, Tianjin University, Tianjin 300354, People's Republic of China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101860133","display_name":"Yufan Li","orcid":"https://orcid.org/0000-0001-8191-2738"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu-Fan Li","raw_affiliation_strings":["School of Science, Sun Yat-sen University, Shenzhen 518107, People\u2019s Republic of China","School of Science, Sun Yat-sen University, Shenzhen 518107, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Sun Yat-sen University, Shenzhen 518107, People\u2019s Republic of China","institution_ids":["https://openalex.org/I157773358"]},{"raw_affiliation_string":"School of Science, Sun Yat-sen University, Shenzhen 518107, People's Republic of China","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066902317","display_name":"Xin-He Miao","orcid":null},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinhe Miao","raw_affiliation_strings":["School of Mathematics, Tianjin University, Tianjin 300354, People\u2019s Republic of China","School of Mathematics, Tianjin University, Tianjin 300354, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Tianjin University, Tianjin 300354, People\u2019s Republic of China","institution_ids":["https://openalex.org/I162868743"]},{"raw_affiliation_string":"School of Mathematics, Tianjin University, Tianjin 300354, People's Republic of China","institution_ids":["https://openalex.org/I162868743"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5050088762"],"corresponding_institution_ids":["https://openalex.org/I162868743"],"apc_list":null,"apc_paid":null,"fwci":1.6618,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.83155397,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"44","issue":"2","first_page":"530","last_page":"558"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9998000264167786,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9876000285148621,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9794999957084656,"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":0.8459348678588867},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.6494539976119995},{"id":"https://openalex.org/keywords/symmetric-tensor","display_name":"Symmetric tensor","score":0.5359889268875122},{"id":"https://openalex.org/keywords/solution-set","display_name":"Solution set","score":0.4715963304042816},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.43566328287124634},{"id":"https://openalex.org/keywords/tensor-field","display_name":"Tensor field","score":0.42376798391342163},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42185696959495544},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3946608901023865},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.3931836485862732},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.30198347568511963},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2446298599243164},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07430797815322876}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8459348678588867},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6494539976119995},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.5359889268875122},{"id":"https://openalex.org/C60033838","wikidata":"https://www.wikidata.org/wiki/Q1751685","display_name":"Solution set","level":3,"score":0.4715963304042816},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.43566328287124634},{"id":"https://openalex.org/C166077713","wikidata":"https://www.wikidata.org/wiki/Q1758924","display_name":"Tensor field","level":3,"score":0.42376798391342163},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42185696959495544},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3946608901023865},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.3931836485862732},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.30198347568511963},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2446298599243164},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07430797815322876},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1476733","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1476733","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/G2099803721","display_name":null,"funder_award_id":"11871051","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5554647668","display_name":null,"funder_award_id":"11901600","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6328561046","display_name":null,"funder_award_id":"12171357","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":38,"referenced_works":["https://openalex.org/W175892734","https://openalex.org/W1544284532","https://openalex.org/W1967073510","https://openalex.org/W1985354601","https://openalex.org/W2005222333","https://openalex.org/W2005347459","https://openalex.org/W2012593053","https://openalex.org/W2037409933","https://openalex.org/W2072477022","https://openalex.org/W2090208105","https://openalex.org/W2090967418","https://openalex.org/W2094247338","https://openalex.org/W2098139002","https://openalex.org/W2102107417","https://openalex.org/W2120001551","https://openalex.org/W2133937084","https://openalex.org/W2151293435","https://openalex.org/W2154650988","https://openalex.org/W2204354727","https://openalex.org/W2208629516","https://openalex.org/W2222111999","https://openalex.org/W2266798071","https://openalex.org/W2582681631","https://openalex.org/W2747026371","https://openalex.org/W2749459105","https://openalex.org/W2750706968","https://openalex.org/W2754476852","https://openalex.org/W2792710073","https://openalex.org/W2800947015","https://openalex.org/W2915529134","https://openalex.org/W2960489998","https://openalex.org/W2963018695","https://openalex.org/W2964016968","https://openalex.org/W2966845367","https://openalex.org/W2967514193","https://openalex.org/W2968579382","https://openalex.org/W4301791716","https://openalex.org/W4378195498"],"related_works":["https://openalex.org/W3050972237","https://openalex.org/W3214531188","https://openalex.org/W2055544189","https://openalex.org/W4353081986","https://openalex.org/W2009425602","https://openalex.org/W2060415987","https://openalex.org/W2254082118","https://openalex.org/W1887380982","https://openalex.org/W336908258","https://openalex.org/W3095959603"],"abstract_inverted_index":{".In":[0],"this":[1],"paper,":[2],"we":[3,101,129],"consider":[4],"the":[5,29,33,43,48,54,58,66,69,79,84,87,93,108,112,118,125,146,150,160,165,174,178,183,187,211],"least":[6,109,126,147,166],"element":[7,110,127,148,167],"problem":[8,61],"of":[9,14,17,57,68,78,111,121,133,136,149,173,186,219],"a":[10,15,21,26,40,75,97,131,171,190],"nonnegative":[11],"solution":[12,172,185],"set":[13,30,49,89,151],"system":[16,135],"inequalities":[18],"defined":[19,38],"by":[20,39,116],"homogeneous":[22,34],"polynomial":[23,35],"mapping":[24,36],"and":[25,92,143,201],"vector.":[27],"In":[28],"under":[31,50,83],"consideration,":[32],"is":[37,46,52,74,90,96,163,169,214],"tensor.":[41],"When":[42,159],"tensor":[44,59,94,137,161,220],"involved":[45,95,162],"square,":[47,164],"consideration":[51],"just":[53],"feasible":[55],"region":[56],"complementarity":[60,217],"(TCP).":[62],"We":[63],"first":[64],"introduce":[65],"concept":[67],"generalized":[70,98],"\\(Z\\)":[71,80,99,191],"-tensor,":[72,100,192],"which":[73],"natural":[76],"generalization":[77],"-tensor.":[81],"Then,":[82],"assumption":[85],"that":[86,145,210],"considered":[88,113],"nonempty":[91],"propose":[102],"an":[103],"iterative":[104],"method":[105,194,213],"for":[106,181],"finding":[107,182],"set.":[114],"Specifically,":[115],"recognizing":[117],"position":[119],"indices":[120,142],"positive":[122],"components":[123],"in":[124],"continuously,":[128],"solve":[130],"series":[132],"lower-dimensional":[134],"equations":[138],"corresponding":[139],"to":[140],"these":[141],"prove":[144],"can":[152],"be":[153],"obtained":[154,168],"within":[155],"finite":[156],"step":[157],"iterations.":[158],"also":[170],"TCP.":[175],"Compared":[176],"with":[177,189],"existing":[179],"methods":[180],"least-element":[184],"TCP":[188],"our":[193],"does":[195],"not":[196],"require":[197],"any":[198],"additional":[199],"assumptions":[200],"has":[202],"lower":[203],"computational":[204],"cost.":[205],"Preliminary":[206],"numerical":[207],"experiments":[208],"show":[209],"proposed":[212],"effective.Keywordsleast":[215],"elementtensor":[216],"problemsystem":[218],"equationsMSC":[221],"codes90C3365K15":[222]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}