{"id":"https://openalex.org/W1974962384","doi":"https://doi.org/10.1007/s10107-008-0240-y","title":"Semidefinite representation of convex sets","display_name":"Semidefinite representation of convex sets","publication_year":2008,"publication_date":"2008-08-20","ids":{"openalex":"https://openalex.org/W1974962384","doi":"https://doi.org/10.1007/s10107-008-0240-y","mag":"1974962384"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-008-0240-y","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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/P4310319965","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Springer Nature","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":"https://arxiv.org/pdf/0705.4068","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080005590","display_name":"J. William Helton","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":"J. William Helton","raw_affiliation_strings":["University of California at San Diego, Department of Mathematics, 9500 Gilman Drive, 92093, La Jolla, CA, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"University of California at San Diego, Department of Mathematics, 9500 Gilman Drive, 92093, La Jolla, CA, USA#TAB#","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","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":false,"raw_author_name":"Jiawang Nie","raw_affiliation_strings":["University of California at San Diego, Department of Mathematics, 9500 Gilman Drive, 92093, La Jolla, CA, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"University of California at San Diego, Department of Mathematics, 9500 Gilman Drive, 92093, La Jolla, CA, USA#TAB#","institution_ids":["https://openalex.org/I36258959"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890,"provenance":"doaj"},"apc_paid":null,"fwci":10.406,"has_fulltext":false,"cited_by_count":162,"citation_normalized_percentile":{"value":0.999436,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"122","issue":"1","first_page":"21","last_page":"64"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9999,"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":0.9999,"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":0.9965,"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/T11236","display_name":"Control Systems and Identification","score":0.9942,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite Programming","score":0.7346642},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.62111527}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.81442976},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.7346642},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.680118},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.6653844},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.62111527},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6097579},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5004556},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.46473718},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.40276805},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32125682},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13477737},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.10880676},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.07821146},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.07098371},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06848651},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-008-0240-y","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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/P4310319965","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Springer Nature","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/0705.4068","pdf_url":"https://arxiv.org/pdf/0705.4068","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":null,"pdf_url":"https://arxiv.org/pdf/0705.4068v1.pdf","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/0705.4068","pdf_url":"https://arxiv.org/pdf/0705.4068","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":30,"referenced_works":["https://openalex.org/W1507415131","https://openalex.org/W1539838732","https://openalex.org/W1568307856","https://openalex.org/W1591868040","https://openalex.org/W1632601927","https://openalex.org/W1964962380","https://openalex.org/W1967344706","https://openalex.org/W1970699014","https://openalex.org/W197661341","https://openalex.org/W2001033871","https://openalex.org/W2019514156","https://openalex.org/W2022806724","https://openalex.org/W2024340911","https://openalex.org/W2025202934","https://openalex.org/W2026578200","https://openalex.org/W2083449425","https://openalex.org/W2106290082","https://openalex.org/W2137508197","https://openalex.org/W2153170581","https://openalex.org/W2296319761","https://openalex.org/W2495457432","https://openalex.org/W2962725330","https://openalex.org/W3021722416","https://openalex.org/W4250589301","https://openalex.org/W4254742099","https://openalex.org/W4255442211","https://openalex.org/W4293259004","https://openalex.org/W4299599836","https://openalex.org/W654059483","https://openalex.org/W99708544"],"related_works":["https://openalex.org/W4390640000","https://openalex.org/W4312206320","https://openalex.org/W2803118069","https://openalex.org/W2617248812","https://openalex.org/W2160052563","https://openalex.org/W2126408684","https://openalex.org/W2115832833","https://openalex.org/W2064377790","https://openalex.org/W2040676043","https://openalex.org/W1544933314"],"abstract_inverted_index":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W1974962384","counts_by_year":[{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":13},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":14},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":6}],"updated_date":"2025-01-06T02:03:54.009646","created_date":"2016-06-24"}