{"id":"https://openalex.org/W2971468916","doi":"https://doi.org/10.1137/18m1181262","title":"Generalized Differentiation of Probability Functions Acting on an Infinite System of Constraints","display_name":"Generalized Differentiation of Probability Functions Acting on an Infinite System of Constraints","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2971468916","doi":"https://doi.org/10.1137/18m1181262","mag":"2971468916"},"language":"en","primary_location":{"id":"doi:10.1137/18m1181262","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1181262","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080745391","display_name":"Wim van Ackooij","orcid":"https://orcid.org/0000-0002-9943-3572"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wim van Ackooij","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5044297986","display_name":"Pedro P\u00e9rez-Aros","orcid":"https://orcid.org/0000-0002-8756-3011"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pedro P\u00e9rez-Aros","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-8756-3011","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7795,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.8608238,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"29","issue":"3","first_page":"2179","last_page":"2210"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8045396208763123},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.7497743368148804},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.5459694862365723},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5355918407440186},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5246888995170593},{"id":"https://openalex.org/keywords/probability-mass-function","display_name":"Probability mass function","score":0.5070245265960693},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.347359836101532},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.1897369623184204},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18506765365600586},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10576927661895752}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8045396208763123},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.7497743368148804},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.5459694862365723},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5355918407440186},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5246888995170593},{"id":"https://openalex.org/C197096303","wikidata":"https://www.wikidata.org/wiki/Q869887","display_name":"Probability mass function","level":3,"score":0.5070245265960693},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.347359836101532},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.1897369623184204},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18506765365600586},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10576927661895752},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/18m1181262","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1181262","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.800000011920929,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G8024461642","display_name":null,"funder_award_id":"1190110","funder_id":"https://openalex.org/F4320338073","funder_display_name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico"}],"funders":[{"id":"https://openalex.org/F4320338073","display_name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico","ror":"https://ror.org/02ap3w078"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W1459610841","https://openalex.org/W1570578847","https://openalex.org/W1971092617","https://openalex.org/W1972577527","https://openalex.org/W1979512503","https://openalex.org/W1981435784","https://openalex.org/W1982661895","https://openalex.org/W1989755892","https://openalex.org/W1993708577","https://openalex.org/W1997808314","https://openalex.org/W2003777645","https://openalex.org/W2007668370","https://openalex.org/W2008685729","https://openalex.org/W2010811500","https://openalex.org/W2017450869","https://openalex.org/W2029225872","https://openalex.org/W2036529462","https://openalex.org/W2041977479","https://openalex.org/W2053391173","https://openalex.org/W2053481037","https://openalex.org/W2055661359","https://openalex.org/W2056940756","https://openalex.org/W2057382113","https://openalex.org/W2059696208","https://openalex.org/W2066778083","https://openalex.org/W2069374819","https://openalex.org/W2090364210","https://openalex.org/W2090905570","https://openalex.org/W2093304942","https://openalex.org/W2093529512","https://openalex.org/W2095564588","https://openalex.org/W2095861442","https://openalex.org/W2099506495","https://openalex.org/W2105378603","https://openalex.org/W2118382239","https://openalex.org/W2130117043","https://openalex.org/W2139869783","https://openalex.org/W2142261996","https://openalex.org/W2143514150","https://openalex.org/W2151140685","https://openalex.org/W2156688308","https://openalex.org/W2164499670","https://openalex.org/W2167412190","https://openalex.org/W2261073569","https://openalex.org/W2346910096","https://openalex.org/W2375159103","https://openalex.org/W2400155314","https://openalex.org/W2500599198","https://openalex.org/W2569380384","https://openalex.org/W2622903347","https://openalex.org/W2751459826","https://openalex.org/W2763608097","https://openalex.org/W2764133341","https://openalex.org/W2788729665","https://openalex.org/W2911593290","https://openalex.org/W2913806414"],"related_works":["https://openalex.org/W2414667732","https://openalex.org/W4249885815","https://openalex.org/W2340232283","https://openalex.org/W2136538477","https://openalex.org/W2183396261","https://openalex.org/W4300998569","https://openalex.org/W4233290694","https://openalex.org/W3037024381","https://openalex.org/W118404227","https://openalex.org/W2058696512"],"abstract_inverted_index":{"In":[0,85],"decision-making":[1],"problems":[2],"under":[3],"uncertainty,":[4],"probability":[5,21,51,77,94],"constraints":[6],"are":[7],"a":[8,24],"valuable":[9],"tool":[10],"for":[11,65,101],"expressing":[12],"safety":[13],"of":[14,23,27,52,61,83,92],"decisions.":[15],"They":[16],"result":[17],"from":[18,38],"taking":[19],"the":[20,32,50,53,59,62,102],"measure":[22],"given":[25],"set":[26],"random":[28],"inequalities":[29],"depending":[30],"on":[31,80],"decision":[33],"vector.":[34],"When":[35],"uncertainty":[36,63],"results":[37],"two":[39],"different":[40],"sources,":[41],"unequally":[42],"known,":[43],"it":[44],"becomes":[45],"intuitively":[46],"appealing":[47],"to":[48,58,76],"consider":[49],"worst":[54],"case":[55],"with":[56],"respect":[57],"part":[60],"vector":[64],"which":[66],"little":[67],"information":[68],"was":[69],"available.":[70],"This":[71],"and":[72],"other":[73],"models":[74],"lead":[75],"functions":[78],"acting":[79],"infinite":[81],"systems":[82],"constraints.":[84],"this":[86],"paper":[87],"we":[88],"study":[89],"generalized":[90],"(sub)differentiation":[91],"such":[93],"functions.":[95],"We":[96],"also":[97],"develop":[98],"explicit":[99],"formulae":[100],"subdifferentials":[103],"that":[104],"should":[105],"prove":[106],"useful":[107],"in":[108,112],"first-order":[109],"methods":[110],"or":[111],"formulating":[113],"optimality":[114],"conditions.":[115]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}