{"id":"https://openalex.org/W2727040141","doi":"https://doi.org/10.1007/978-0-387-74759-0_141","title":"Duality Theory: Monoduality in Convex Optimization","display_name":"Duality Theory: Monoduality in Convex Optimization","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2727040141","doi":"https://doi.org/10.1007/978-0-387-74759-0_141","mag":"2727040141"},"language":"en","primary_location":{"id":"doi:10.1007/978-0-387-74759-0_141","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-0-387-74759-0_141","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/A5048360771","display_name":"David Yang Gao","orcid":"https://orcid.org/0000-0002-2245-8050"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"David Yang Gao","raw_affiliation_strings":["Virginia Polytechnic Institute and State University, Blacksburg, USA"],"affiliations":[{"raw_affiliation_string":"Virginia Polytechnic Institute and State University, Blacksburg, USA","institution_ids":["https://openalex.org/I859038795"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5048360771"],"corresponding_institution_ids":["https://openalex.org/I859038795"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.3974175,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"818","last_page":"822"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.7411999702453613,"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":0.7411999702453613,"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":0.7390999794006348,"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/duality","display_name":"Duality (order theory)","score":0.7133815288543701},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.5851263999938965},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48792049288749695},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.46623489260673523},{"id":"https://openalex.org/keywords/conic-optimization","display_name":"Conic optimization","score":0.45999109745025635},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.45620983839035034},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3046080470085144},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09104594588279724}],"concepts":[{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.7133815288543701},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.5851263999938965},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48792049288749695},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.46623489260673523},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.45999109745025635},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.45620983839035034},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3046080470085144},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09104594588279724}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-0-387-74759-0_141","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-0-387-74759-0_141","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":3,"referenced_works":["https://openalex.org/W587390710","https://openalex.org/W1509805685","https://openalex.org/W1518039036"],"related_works":["https://openalex.org/W1605722506","https://openalex.org/W2086459570","https://openalex.org/W4287111675","https://openalex.org/W2053671651","https://openalex.org/W4294993249","https://openalex.org/W3135607674","https://openalex.org/W2026483567","https://openalex.org/W2155425983","https://openalex.org/W3198578815","https://openalex.org/W2610781457"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
