{"id":"https://openalex.org/W2969457913","doi":"https://doi.org/10.1080/10556788.2019.1649672","title":"Stochastic polynomial optimization","display_name":"Stochastic polynomial optimization","publication_year":2019,"publication_date":"2019-08-22","ids":{"openalex":"https://openalex.org/W2969457913","doi":"https://doi.org/10.1080/10556788.2019.1649672","mag":"2969457913"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2019.1649672","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2019.1649672","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","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/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, La Jolla, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100776165","display_name":"Liu Yang","orcid":"https://orcid.org/0000-0002-4072-6581"},"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":"Liu Yang","raw_affiliation_strings":["School of Mathematics and Computational Sciences, Xiangtan University, Xiangtan, Hunan, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Sciences, Xiangtan University, Xiangtan, Hunan, China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071970740","display_name":"Suhan Zhong","orcid":null},"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":"Suhan Zhong","raw_affiliation_strings":["Department of Mathematics, University of California San Diego, La Jolla, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]}]}],"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":null,"apc_paid":null,"fwci":1.2882,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.78378378,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"35","issue":"2","first_page":"329","last_page":"347"},"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":0.9976999759674072,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9954000115394592,"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/stochastic-optimization","display_name":"Stochastic optimization","score":0.7059826254844666},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.6145487427711487},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.608268678188324},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6011385917663574},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.537894606590271},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5338607430458069},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.4907163381576538},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44389185309410095},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.43391352891921997},{"id":"https://openalex.org/keywords/optimization-algorithm","display_name":"Optimization algorithm","score":0.4240555763244629},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1668700873851776},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10866570472717285}],"concepts":[{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.7059826254844666},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.6145487427711487},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.608268678188324},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6011385917663574},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.537894606590271},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5338607430458069},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.4907163381576538},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44389185309410095},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.43391352891921997},{"id":"https://openalex.org/C2987595161","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Optimization algorithm","level":2,"score":0.4240555763244629},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1668700873851776},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10866570472717285},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556788.2019.1649672","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2019.1649672","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W404764422","https://openalex.org/W600148761","https://openalex.org/W1752958389","https://openalex.org/W1964603869","https://openalex.org/W1967073510","https://openalex.org/W1967184028","https://openalex.org/W1967344706","https://openalex.org/W1970515840","https://openalex.org/W1973836753","https://openalex.org/W1974962384","https://openalex.org/W1975273219","https://openalex.org/W1980700045","https://openalex.org/W1983916623","https://openalex.org/W1985650248","https://openalex.org/W1995878217","https://openalex.org/W2000257769","https://openalex.org/W2001334051","https://openalex.org/W2029463628","https://openalex.org/W2039000181","https://openalex.org/W2052557161","https://openalex.org/W2074085031","https://openalex.org/W2084029876","https://openalex.org/W2090967418","https://openalex.org/W2100140125","https://openalex.org/W2133602590","https://openalex.org/W2143514150","https://openalex.org/W2156811188","https://openalex.org/W2787555265","https://openalex.org/W2963470657","https://openalex.org/W2963819442","https://openalex.org/W4247165901","https://openalex.org/W4250589301","https://openalex.org/W4255442211"],"related_works":["https://openalex.org/W1978745259","https://openalex.org/W3127438322","https://openalex.org/W4287330080","https://openalex.org/W1990112656","https://openalex.org/W4283738289","https://openalex.org/W2363855676","https://openalex.org/W2073248645","https://openalex.org/W2152231846","https://openalex.org/W3095130276","https://openalex.org/W195464835"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"stochastic":[3],"optimization":[4,11,33],"problems":[5],"with":[6,13],"polynomials.":[7],"We":[8],"propose":[9],"an":[10],"model":[12],"sample":[14,27],"averages":[15],"and":[16,34],"perturbations.":[17],"The":[18],"Lasserre-type":[19],"Moment-SOS":[20],"relaxations":[21,36],"are":[22,37,41],"used":[23],"to":[24],"solve":[25],"the":[26,32],"average":[28],"optimization.":[29],"Properties":[30],"of":[31],"its":[35],"studied.":[38],"Numerical":[39],"experiments":[40],"presented.":[42]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}