{"id":"https://openalex.org/W2166798101","doi":"https://doi.org/10.1137/050623802","title":"Sums of Squares and Semidefinite Program Relaxations for Polynomial Optimization Problems with Structured Sparsity","display_name":"Sums of Squares and Semidefinite Program Relaxations for Polynomial Optimization Problems with Structured Sparsity","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2166798101","doi":"https://doi.org/10.1137/050623802","mag":"2166798101"},"language":"en","primary_location":{"id":"doi:10.1137/050623802","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050623802","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/A5080255628","display_name":"Hayato Waki","orcid":"https://orcid.org/0000-0002-0531-2201"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hayato Waki","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100333111","display_name":"Sunyoung Kim","orcid":"https://orcid.org/0000-0003-3705-9746"},"institutions":[{"id":"https://openalex.org/I530967","display_name":"Toronto Metropolitan University","ror":"https://ror.org/05g13zd79","country_code":"CA","type":"education","lineage":["https://openalex.org/I530967"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Sunyoung Kim","raw_affiliation_strings":["Department of Mathematics"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics","institution_ids":["https://openalex.org/I530967"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113974670","display_name":"Masakazu Kojima","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Masakazu Kojima","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5113934718","display_name":"Masakazu Muramatsu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Masakazu Muramatsu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5080255628"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":31.2271,"has_fulltext":false,"cited_by_count":461,"citation_normalized_percentile":{"value":0.99925206,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"17","issue":"1","first_page":"218","last_page":"242"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9799000024795532,"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"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9729999899864197,"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/semidefinite-programming","display_name":"Semidefinite programming","score":0.8399180173873901},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7901872396469116},{"id":"https://openalex.org/keywords/explained-sum-of-squares","display_name":"Explained sum of squares","score":0.6669055223464966},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4894484579563141},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4824022054672241},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.42680495977401733},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41817545890808105},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3562812805175781}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.8399180173873901},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7901872396469116},{"id":"https://openalex.org/C49847556","wikidata":"https://www.wikidata.org/wiki/Q3964631","display_name":"Explained sum of squares","level":2,"score":0.6669055223464966},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4894484579563141},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4824022054672241},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.42680495977401733},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41817545890808105},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3562812805175781},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050623802","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050623802","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":[{"id":"https://metadata.un.org/sdg/10","score":0.44999998807907104,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W126279018","https://openalex.org/W1484494266","https://openalex.org/W1563737017","https://openalex.org/W1571966798","https://openalex.org/W1967073510","https://openalex.org/W1967184028","https://openalex.org/W1967344706","https://openalex.org/W1985123706","https://openalex.org/W1989190791","https://openalex.org/W1990659369","https://openalex.org/W1996541174","https://openalex.org/W1997672673","https://openalex.org/W1998648277","https://openalex.org/W2001033871","https://openalex.org/W2011253492","https://openalex.org/W2013621063","https://openalex.org/W2020562473","https://openalex.org/W2029485617","https://openalex.org/W2048221927","https://openalex.org/W2056603712","https://openalex.org/W2065000345","https://openalex.org/W2065053468","https://openalex.org/W2066736759","https://openalex.org/W2069426496","https://openalex.org/W2071143636","https://openalex.org/W2077397558","https://openalex.org/W2085729541","https://openalex.org/W2089465933","https://openalex.org/W2090084096","https://openalex.org/W2103327612","https://openalex.org/W2104842300","https://openalex.org/W2113280143","https://openalex.org/W2140357316","https://openalex.org/W2143474538","https://openalex.org/W2147191663","https://openalex.org/W2153451837","https://openalex.org/W2498144272","https://openalex.org/W2738786117","https://openalex.org/W2962725330","https://openalex.org/W3104001151","https://openalex.org/W4255442211"],"related_works":["https://openalex.org/W2493494838","https://openalex.org/W2963700124","https://openalex.org/W4297923520","https://openalex.org/W2624196447","https://openalex.org/W2077924482","https://openalex.org/W2771160919","https://openalex.org/W4301659259","https://openalex.org/W1571037741","https://openalex.org/W4298028631","https://openalex.org/W2963530480"],"abstract_inverted_index":{"Unconstrained":[0],"and":[1,27,52,75],"inequality":[2],"constrained":[3],"sparse":[4,22],"polynomial":[5],"optimization":[6],"problems":[7,64],"(POPs)":[8],"are":[9,57,65],"considered.":[10],"A":[11],"correlative":[12],"sparsity":[13],"pattern":[14],"graph":[15],"is":[16],"defined":[17],"to":[18,49,67],"find":[19],"a":[20,31],"certain":[21],"structure":[23],"in":[24],"the":[25,39,69,73],"objective":[26],"constraint":[28],"polynomials":[29,46],"of":[30,38,43,72],"POP.":[32],"Based":[33],"on":[34],"this":[35],"graph,":[36],"sets":[37],"supports":[40],"for":[41],"sums":[42],"squares":[44],"(SOS)":[45],"that":[47],"lead":[48],"efficient":[50],"SOS":[51,74],"semidefinite":[53],"program":[54],"(SDP)":[55],"relaxations":[56],"obtained.":[58],"Numerical":[59],"results":[60],"from":[61],"various":[62],"test":[63],"included":[66],"show":[68],"improved":[70],"performance":[71],"SDP":[76],"relaxations.":[77]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":26},{"year":2021,"cited_by_count":25},{"year":2020,"cited_by_count":36},{"year":2019,"cited_by_count":32},{"year":2018,"cited_by_count":33},{"year":2017,"cited_by_count":18},{"year":2016,"cited_by_count":21},{"year":2015,"cited_by_count":25},{"year":2014,"cited_by_count":24},{"year":2013,"cited_by_count":24},{"year":2012,"cited_by_count":22}],"updated_date":"2026-04-24T08:23:43.765630","created_date":"2025-10-10T00:00:00"}
