{"id":"https://openalex.org/W4388456713","doi":"https://doi.org/10.1137/22m1539137","title":"Semidefinite Relaxation Methods for Tensor Absolute Value Equations","display_name":"Semidefinite Relaxation Methods for Tensor Absolute Value Equations","publication_year":2023,"publication_date":"2023-11-07","ids":{"openalex":"https://openalex.org/W4388456713","doi":"https://doi.org/10.1137/22m1539137"},"language":"en","primary_location":{"id":"doi:10.1137/22m1539137","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1539137","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/A5020709130","display_name":"Anwa Zhou","orcid":"https://orcid.org/0000-0002-8453-7651"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Anwa Zhou","raw_affiliation_strings":["Department of Mathematics, Shanghai University, Shanghai 200444, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai University, Shanghai 200444, People\u2019s Republic of China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100398760","display_name":"Kun Liu","orcid":"https://orcid.org/0000-0002-1743-5524"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kun Liu","raw_affiliation_strings":["Department of Mathematics, Shanghai University, Shanghai 200444, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai University, Shanghai 200444, People\u2019s Republic of China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102105118","display_name":"Jinyan Fan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jinyan Fan","raw_affiliation_strings":["School of Mathematical Sciences, and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, People\u2019s Republic of China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5020709130"],"corresponding_institution_ids":["https://openalex.org/I113940042"],"apc_list":null,"apc_paid":null,"fwci":0.4214,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.55871886,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"44","issue":"4","first_page":"1667","last_page":"1692"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9988999962806702,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9986000061035156,"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/mathematics","display_name":"Mathematics","score":0.8794363737106323},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.6705210208892822},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.6632856726646423},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.6247915625572205},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.5579676032066345},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5419436693191528},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4971480667591095},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4870179295539856},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.46989676356315613},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4452798366546631},{"id":"https://openalex.org/keywords/symmetric-tensor","display_name":"Symmetric tensor","score":0.420406699180603},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.418311208486557},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.4139365553855896},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33260589838027954},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2974613904953003},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.2017456293106079},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.192496657371521},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10761970281600952},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.08081451058387756}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8794363737106323},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.6705210208892822},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6632856726646423},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6247915625572205},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.5579676032066345},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5419436693191528},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4971480667591095},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4870179295539856},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.46989676356315613},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4452798366546631},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.420406699180603},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.418311208486557},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.4139365553855896},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33260589838027954},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2974613904953003},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.2017456293106079},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.192496657371521},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10761970281600952},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.08081451058387756},{"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/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1539137","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1539137","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/G2931280968","display_name":null,"funder_award_id":"12271336","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7500400836","display_name":null,"funder_award_id":"11971309","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":49,"referenced_works":["https://openalex.org/W1559197676","https://openalex.org/W1568307856","https://openalex.org/W1964493541","https://openalex.org/W1964603869","https://openalex.org/W1967073510","https://openalex.org/W1967344706","https://openalex.org/W1973411603","https://openalex.org/W1973836753","https://openalex.org/W1978485957","https://openalex.org/W1985650248","https://openalex.org/W2006402206","https://openalex.org/W2013760236","https://openalex.org/W2015508922","https://openalex.org/W2023548950","https://openalex.org/W2039355449","https://openalex.org/W2046904496","https://openalex.org/W2052557161","https://openalex.org/W2053227127","https://openalex.org/W2071550336","https://openalex.org/W2090967418","https://openalex.org/W2134508021","https://openalex.org/W2143920029","https://openalex.org/W2156811188","https://openalex.org/W2160639883","https://openalex.org/W2266798071","https://openalex.org/W2495457432","https://openalex.org/W2615373644","https://openalex.org/W2767311547","https://openalex.org/W2787555265","https://openalex.org/W2945689389","https://openalex.org/W2962705706","https://openalex.org/W2962989821","https://openalex.org/W2963819442","https://openalex.org/W2991612826","https://openalex.org/W3009647459","https://openalex.org/W3013600831","https://openalex.org/W3023939313","https://openalex.org/W3035723705","https://openalex.org/W3037346199","https://openalex.org/W3119965387","https://openalex.org/W3188368100","https://openalex.org/W3217515895","https://openalex.org/W4213158988","https://openalex.org/W4225149655","https://openalex.org/W4255442211","https://openalex.org/W4293809547","https://openalex.org/W4293860921","https://openalex.org/W4299599836","https://openalex.org/W4301491118"],"related_works":["https://openalex.org/W4251428025","https://openalex.org/W2784467519","https://openalex.org/W4289867043","https://openalex.org/W2366459771","https://openalex.org/W2963453621","https://openalex.org/W2043810741","https://openalex.org/W2350707375","https://openalex.org/W2135584473","https://openalex.org/W2377881809","https://openalex.org/W2988424716"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,20,42,60],"consider":[4],"the":[5,23,45,62,95,98],"tensor":[6,13,56],"absolute":[7],"value":[8],"equations":[9],"(TAVEs).":[10],"When":[11,54],"one":[12],"is":[14,34,47,57],"row":[15,35,58],"diagonal":[16,36],"with":[17,39],"odd":[18],"order,":[19,41],"show":[21,94],"that":[22,44],"TAVEs":[24,46,63],"can":[25,76],"be":[26,77],"reduced":[27],"to":[28,49],"an":[29],"algebraic":[30],"equation;":[31],"when":[32],"it":[33],"and":[37],"nonsingular":[38],"even":[40],"prove":[43],"equivalent":[48],"a":[50],"polynomial":[51,66],"complementary":[52],"problem.":[53],"no":[55],"diagonal,":[59],"formulate":[61],"equivalently":[64],"as":[65],"optimization":[67],"problems":[68],"in":[69],"two":[70],"different":[71],"ways.":[72],"Each":[73],"of":[74,82,97],"them":[75],"solved":[78],"by":[79],"Lasserre\u2019s":[80],"hierarchy":[81],"semidefinite":[83],"relaxations.":[84],"The":[85],"finite":[86],"convergence":[87],"properties":[88],"are":[89],"also":[90],"discussed.":[91],"Numerical":[92],"experiments":[93],"efficiency":[96],"proposed":[99],"methods.":[100]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}