{"id":"https://openalex.org/W3992437","doi":"https://doi.org/10.1007/978-0-387-74759-0_139","title":"Duality for Semidefinite Programming","display_name":"Duality for Semidefinite Programming","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W3992437","doi":"https://doi.org/10.1007/978-0-387-74759-0_139","mag":"3992437"},"language":"en","primary_location":{"id":"doi:10.1007/978-0-387-74759-0_139","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-0-387-74759-0_139","pdf_url":null,"source":{"id":"https://openalex.org/S4306509378","display_name":"Encyclopedia of Optimization","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Encyclopedia of Optimization","raw_type":"book-chapter"},"type":"book-chapter","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/A5061777786","display_name":"Henry Wolkowicz","orcid":"https://orcid.org/0000-0003-1572-3060"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Henry Wolkowicz","raw_affiliation_strings":["Department Combinatorics and Optimization, University Waterloo, Waterloo, Canada"],"affiliations":[{"raw_affiliation_string":"Department Combinatorics and Optimization, University Waterloo, Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5061777786"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"811","last_page":"814"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"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":0.9995999932289124,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9929999709129333,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9779000282287598,"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":0.8617435693740845},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.7882468700408936},{"id":"https://openalex.org/keywords/semidefinite-embedding","display_name":"Semidefinite embedding","score":0.6033814549446106},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.4363902807235718},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4119972884654999},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3854031562805176},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37615060806274414},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3394755721092224},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2235422134399414},{"id":"https://openalex.org/keywords/quadratically-constrained-quadratic-program","display_name":"Quadratically constrained quadratic program","score":0.16243088245391846},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.11382463574409485},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.039829909801483154}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.8617435693740845},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.7882468700408936},{"id":"https://openalex.org/C206818286","wikidata":"https://www.wikidata.org/wiki/Q7449403","display_name":"Semidefinite embedding","level":4,"score":0.6033814549446106},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.4363902807235718},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4119972884654999},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3854031562805176},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37615060806274414},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3394755721092224},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2235422134399414},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.16243088245391846},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.11382463574409485},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.039829909801483154}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-0-387-74759-0_139","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-0-387-74759-0_139","pdf_url":null,"source":{"id":"https://openalex.org/S4306509378","display_name":"Encyclopedia of Optimization","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Encyclopedia of Optimization","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1488876970","https://openalex.org/W1595903022","https://openalex.org/W2011475894","https://openalex.org/W2076767912","https://openalex.org/W2080359169","https://openalex.org/W2092569137","https://openalex.org/W2795674018"],"related_works":["https://openalex.org/W1964626732","https://openalex.org/W1972790638","https://openalex.org/W2082156532","https://openalex.org/W2949333496","https://openalex.org/W2382898669","https://openalex.org/W1973754113","https://openalex.org/W2743699369","https://openalex.org/W2070126296","https://openalex.org/W2111625598","https://openalex.org/W3111265261"],"abstract_inverted_index":null,"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}