{"id":"https://openalex.org/W3177747327","doi":"https://doi.org/10.1007/s10208-021-09526-8","title":"The Saddle Point Problem of Polynomials","display_name":"The Saddle Point Problem of Polynomials","publication_year":2021,"publication_date":"2021-07-09","ids":{"openalex":"https://openalex.org/W3177747327","doi":"https://doi.org/10.1007/s10208-021-09526-8","mag":"3177747327"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-021-09526-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-021-09526-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-021-09526-8.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10208-021-09526-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018024598","display_name":"Jiawang Nie","orcid":"https://orcid.org/0000-0003-2637-8274"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jiawang Nie","raw_affiliation_strings":["Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, 92093, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, 92093, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049795713","display_name":"Zi Yang","orcid":"https://orcid.org/0000-0003-1048-9869"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zi Yang","raw_affiliation_strings":["Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, 92093, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, 92093, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034610167","display_name":"Guangming Zhou","orcid":"https://orcid.org/0000-0002-7427-1781"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guangming Zhou","raw_affiliation_strings":["School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan, China","institution_ids":["https://openalex.org/I4610292"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018024598"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":3.1197,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.91065446,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"22","issue":"4","first_page":"1133","last_page":"1169"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"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":0.9998000264167786,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9993000030517578,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9979000091552734,"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":0.8516754508018494},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.8058127164840698},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.6692138910293579},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.49860143661499023},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.44743648171424866},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.44338294863700867},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3795158267021179},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3697407841682434},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3493436872959137},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.19717487692832947},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08659252524375916}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8516754508018494},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.8058127164840698},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.6692138910293579},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.49860143661499023},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.44743648171424866},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.44338294863700867},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3795158267021179},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3697407841682434},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3493436872959137},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.19717487692832947},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08659252524375916},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10208-021-09526-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-021-09526-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-021-09526-8.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10208-021-09526-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-021-09526-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-021-09526-8.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1117093733","display_name":null,"funder_award_id":"1417985","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4120529948","display_name":null,"funder_award_id":"DMS-1417985","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8079806728","display_name":null,"funder_award_id":"1619973","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8956530757","display_name":null,"funder_award_id":"DMS-1619973","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3177747327.pdf","grobid_xml":"https://content.openalex.org/works/W3177747327.grobid-xml"},"referenced_works_count":62,"referenced_works":["https://openalex.org/W32532385","https://openalex.org/W131296717","https://openalex.org/W404764422","https://openalex.org/W653291882","https://openalex.org/W1519983590","https://openalex.org/W1525854150","https://openalex.org/W1539838732","https://openalex.org/W1543064558","https://openalex.org/W1570787829","https://openalex.org/W1574151794","https://openalex.org/W1578630563","https://openalex.org/W1583497301","https://openalex.org/W1679815041","https://openalex.org/W1964603869","https://openalex.org/W1967073510","https://openalex.org/W1967184028","https://openalex.org/W1967344706","https://openalex.org/W1973132297","https://openalex.org/W1973836753","https://openalex.org/W1981112674","https://openalex.org/W1985650248","https://openalex.org/W1991813962","https://openalex.org/W2015508922","https://openalex.org/W2016056788","https://openalex.org/W2020123437","https://openalex.org/W2021129860","https://openalex.org/W2021548137","https://openalex.org/W2052557161","https://openalex.org/W2066979034","https://openalex.org/W2069764498","https://openalex.org/W2071727942","https://openalex.org/W2071940220","https://openalex.org/W2072992931","https://openalex.org/W2084845949","https://openalex.org/W2085963752","https://openalex.org/W2086455601","https://openalex.org/W2089559088","https://openalex.org/W2090967418","https://openalex.org/W2092663520","https://openalex.org/W2092851214","https://openalex.org/W2093850840","https://openalex.org/W2113940215","https://openalex.org/W2128324713","https://openalex.org/W2165281529","https://openalex.org/W2167360454","https://openalex.org/W2245131330","https://openalex.org/W2330024298","https://openalex.org/W2422300559","https://openalex.org/W2492629073","https://openalex.org/W2498144272","https://openalex.org/W2514227992","https://openalex.org/W2561746749","https://openalex.org/W2963586744","https://openalex.org/W2963627984","https://openalex.org/W2963819442","https://openalex.org/W2972701999","https://openalex.org/W4234761190","https://openalex.org/W4243539849","https://openalex.org/W4244593923","https://openalex.org/W4255442211","https://openalex.org/W4299599836","https://openalex.org/W6959167814"],"related_works":["https://openalex.org/W4236459141","https://openalex.org/W4205304778","https://openalex.org/W2020252434","https://openalex.org/W73248859","https://openalex.org/W2584253892","https://openalex.org/W2350324449","https://openalex.org/W119381072","https://openalex.org/W2034033896","https://openalex.org/W2094891943","https://openalex.org/W4240399920"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"studies":[3],"the":[4],"saddle":[5,16,43,64],"point":[6],"problem":[7],"of":[8,25,55],"polynomials.":[9],"We":[10],"give":[11],"an":[12],"algorithm":[13,46,67],"for":[14],"computing":[15],"points.":[17],"It":[18],"is":[19,62],"based":[20],"on":[21,32],"solving":[22,51],"Lasserre\u2019s":[23],"hierarchy":[24,54],"semidefinite":[26,57],"relaxations.":[27],"Under":[28],"some":[29],"genericity":[30],"assumptions":[31],"defining":[33],"polynomials,":[34],"we":[35],"show":[36],"that:":[37],"(i)":[38],"if":[39,60],"there":[40,61],"exists":[41],"a":[42,52],"point,":[44,65],"our":[45,66],"can":[47,68],"get":[48],"one":[49],"by":[50],"finite":[53],"Lasserre-type":[56],"relaxations;":[58],"(ii)":[59],"no":[63],"detect":[69],"its":[70],"nonexistence.":[71]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}