{"id":"https://openalex.org/W1998611061","doi":"https://doi.org/10.1137/070700413","title":"Subdifferential Calculus Rules in Convex Analysis: A Unifying Approach Via Pointwise Supremum Functions","display_name":"Subdifferential Calculus Rules in Convex Analysis: A Unifying Approach Via Pointwise Supremum Functions","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1998611061","doi":"https://doi.org/10.1137/070700413","mag":"1998611061"},"language":"en","primary_location":{"id":"doi:10.1137/070700413","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070700413","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10045/75119","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048640201","display_name":"Abderrahim Hantoute","orcid":"https://orcid.org/0000-0002-7347-048X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. Hantoute","raw_affiliation_strings":["[email\u00a0protected]#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[email\u00a0protected]#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100715600","display_name":"Marco A. L\u00f3pez","orcid":"https://orcid.org/0000-0002-0619-9618"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. A. L\u00f3pez","raw_affiliation_strings":["marco.antonio@ua.es#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"marco.antonio@ua.es#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034884075","display_name":"Constantin Z\u0103linescu","orcid":"https://orcid.org/0000-0001-8461-818X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C. Z\u0103linescu","raw_affiliation_strings":["zalinesc@uaic.ro#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"zalinesc@uaic.ro#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.0865,"has_fulltext":true,"cited_by_count":102,"citation_normalized_percentile":{"value":0.96972466,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"19","issue":"2","first_page":"863","last_page":"882"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9966999888420105,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9678999781608582,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.8720782995223999},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8536337614059448},{"id":"https://openalex.org/keywords/infimum-and-supremum","display_name":"Infimum and supremum","score":0.7090822458267212},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.698437511920929},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.5244201421737671},{"id":"https://openalex.org/keywords/proper-convex-function","display_name":"Proper convex function","score":0.5010640621185303},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.46989011764526367},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.4372102618217468},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4260711073875427},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4131772220134735},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3647426664829254},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35337939858436584},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.27202871441841125},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24378007650375366}],"concepts":[{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.8720782995223999},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8536337614059448},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.7090822458267212},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.698437511920929},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.5244201421737671},{"id":"https://openalex.org/C50862404","wikidata":"https://www.wikidata.org/wiki/Q3075259","display_name":"Proper convex function","level":5,"score":0.5010640621185303},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.46989011764526367},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.4372102618217468},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4260711073875427},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4131772220134735},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3647426664829254},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35337939858436584},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.27202871441841125},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24378007650375366},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/070700413","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070700413","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"},{"id":"pmh:oai:dnet:ruarepositor::375fbdd0d32ab1938896f771ca33cd4a","is_oa":true,"landing_page_url":"http://hdl.handle.net/10045/75119","pdf_url":"http://hdl.handle.net/10045/75119","source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:dnet:ruarepositor::375fbdd0d32ab1938896f771ca33cd4a","is_oa":true,"landing_page_url":"http://hdl.handle.net/10045/75119","pdf_url":"http://hdl.handle.net/10045/75119","source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W1998611061.pdf"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W83112366","https://openalex.org/W158233626","https://openalex.org/W251840536","https://openalex.org/W1493492050","https://openalex.org/W1499439642","https://openalex.org/W1553702074","https://openalex.org/W1577338488","https://openalex.org/W1974297248","https://openalex.org/W1988627816","https://openalex.org/W1989655633","https://openalex.org/W2026769313","https://openalex.org/W2078395326","https://openalex.org/W2081607835","https://openalex.org/W2101690310","https://openalex.org/W2110041091","https://openalex.org/W2114605231","https://openalex.org/W2116775748","https://openalex.org/W2329743287","https://openalex.org/W2405879537","https://openalex.org/W2530242261","https://openalex.org/W2553512576","https://openalex.org/W4250395145","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W868123585","https://openalex.org/W4311073519","https://openalex.org/W4297909578","https://openalex.org/W4214969932","https://openalex.org/W3122270629","https://openalex.org/W2046751904","https://openalex.org/W4320176170","https://openalex.org/W2032704525","https://openalex.org/W1998611061","https://openalex.org/W2805356302"],"abstract_inverted_index":{"We":[0],"provide":[1],"a":[2,22],"rule":[3,68],"to":[4],"calculate":[5],"the":[6,10,37,48,53,59],"subdifferential":[7],"set":[8,50],"of":[9,13,17,36,70],"pointwise":[11],"supremum":[12,54],"an":[14],"arbitrary":[15],"family":[16],"convex":[18,25],"functions":[19,39],"defined":[20],"on":[21,47,51,58],"real":[23],"locally":[24],"topological":[26],"vector":[27],"space.":[28],"Our":[29],"formula":[30],"is":[31,55],"given":[32],"exclusively":[33],"in":[34],"terms":[35],"data":[38],"and":[40,81],"does":[41],"not":[42],"require":[43],"any":[44],"assumption":[45],"either":[46],"index":[49],"which":[52],"taken":[56],"or":[57],"involved":[60],"functions.":[61],"Some":[62],"other":[63],"calculus":[64],"rules,":[65],"namely":[66],"chain":[67],"formulas":[69],"standard":[71],"type,":[72],"are":[73],"obtained":[74],"from":[75],"our":[76],"main":[77],"result":[78],"via":[79],"new":[80],"direct":[82],"proofs.":[83]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":10}],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2025-10-10T00:00:00"}