{"id":"https://openalex.org/W2398770","doi":"https://doi.org/10.1007/978-3-642-68874-4_15","title":"Generalized Subgradients in Mathematical Programming","display_name":"Generalized Subgradients in Mathematical Programming","publication_year":1983,"publication_date":"1983-01-01","ids":{"openalex":"https://openalex.org/W2398770","doi":"https://doi.org/10.1007/978-3-642-68874-4_15","mag":"2398770"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-68874-4_15","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-68874-4_15","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming The State of the Art","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/A5046903273","display_name":"R. T. Rockafellar","orcid":"https://orcid.org/0000-0003-1703-5069"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"R. T. Rockafellar","raw_affiliation_strings":["Department of Mathematics, University of Washington, C138 Padelford Hall, GN-50, Seattle, WA, 98195, USA","Department of Mathematics, University of Washington, Seattle, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Washington, C138 Padelford Hall, GN-50, Seattle, WA, 98195, USA","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"Department of Mathematics, University of Washington, Seattle, USA#TAB#","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5046903273"],"corresponding_institution_ids":["https://openalex.org/I201448701"],"apc_list":null,"apc_paid":null,"fwci":3.4645,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.90268456,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"368","last_page":"390"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9984999895095825,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9984999895095825,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983000159263611,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.972000002861023,"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/sort","display_name":"sort","score":0.7593942880630493},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.7222265601158142},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.560408890247345},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5473608374595642},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5281184911727905},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3870570957660675},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.14299920201301575},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09148034453392029},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.08992001414299011}],"concepts":[{"id":"https://openalex.org/C88548561","wikidata":"https://www.wikidata.org/wiki/Q347599","display_name":"sort","level":2,"score":0.7593942880630493},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.7222265601158142},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.560408890247345},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5473608374595642},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5281184911727905},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3870570957660675},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.14299920201301575},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09148034453392029},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.08992001414299011},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","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:10.1007/978-3-642-68874-4_15","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-68874-4_15","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming The State of the Art","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":58,"referenced_works":["https://openalex.org/W160520070","https://openalex.org/W197936677","https://openalex.org/W585015008","https://openalex.org/W1964244351","https://openalex.org/W1964379255","https://openalex.org/W1966480644","https://openalex.org/W1968662484","https://openalex.org/W1976086748","https://openalex.org/W1993132035","https://openalex.org/W1994126718","https://openalex.org/W1997015026","https://openalex.org/W2000985550","https://openalex.org/W2001492912","https://openalex.org/W2003678121","https://openalex.org/W2006476326","https://openalex.org/W2007919556","https://openalex.org/W2007952788","https://openalex.org/W2017697298","https://openalex.org/W2025475099","https://openalex.org/W2034145183","https://openalex.org/W2037091587","https://openalex.org/W2044470832","https://openalex.org/W2047102661","https://openalex.org/W2050475426","https://openalex.org/W2051651878","https://openalex.org/W2051903991","https://openalex.org/W2053661713","https://openalex.org/W2060363103","https://openalex.org/W2061928882","https://openalex.org/W2063186190","https://openalex.org/W2067547116","https://openalex.org/W2073431727","https://openalex.org/W2083398653","https://openalex.org/W2087833745","https://openalex.org/W2088786428","https://openalex.org/W2091992858","https://openalex.org/W2094181650","https://openalex.org/W2095893697","https://openalex.org/W2097273628","https://openalex.org/W2107943026","https://openalex.org/W2110041091","https://openalex.org/W2116775748","https://openalex.org/W2136361262","https://openalex.org/W2139160710","https://openalex.org/W2143279738","https://openalex.org/W2161074649","https://openalex.org/W2223181934","https://openalex.org/W2293835388","https://openalex.org/W2363360759","https://openalex.org/W2484906811","https://openalex.org/W2489197912","https://openalex.org/W4211177721","https://openalex.org/W4237662599","https://openalex.org/W4241039954","https://openalex.org/W4244058206","https://openalex.org/W4244637133","https://openalex.org/W4249667877","https://openalex.org/W6641241825"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W4327738859","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2795367102","https://openalex.org/W4255905436","https://openalex.org/W2072554997","https://openalex.org/W108799873","https://openalex.org/W2963676028"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}