{"id":"https://openalex.org/W3006398378","doi":"https://doi.org/10.1007/s10957-020-01634-9","title":"Gradient Formulae for Nonlinear Probabilistic Constraints with Non-convex Quadratic Forms","display_name":"Gradient Formulae for Nonlinear Probabilistic Constraints with Non-convex Quadratic Forms","publication_year":2020,"publication_date":"2020-02-12","ids":{"openalex":"https://openalex.org/W3006398378","doi":"https://doi.org/10.1007/s10957-020-01634-9","mag":"3006398378"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-020-01634-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-020-01634-9","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","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":[{"id":"https://openalex.org/I4210143116","display_name":"\u00c9lectricit\u00e9 de France (France)","ror":"https://ror.org/03wb8xz10","country_code":"FR","type":"company","lineage":["https://openalex.org/I4210143116"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Wim van Ackooij","raw_affiliation_strings":["\u00c9lectricit\u00e9 de France - EDF R&D, Pisa, Italy"],"raw_orcid":"https://orcid.org/0000-0002-9943-3572","affiliations":[{"raw_affiliation_string":"\u00c9lectricit\u00e9 de France - EDF R&D, Pisa, Italy","institution_ids":["https://openalex.org/I4210143116"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044297986","display_name":"Pedro P\u00e9rez-Aros","orcid":"https://orcid.org/0000-0002-8756-3011"},"institutions":[{"id":"https://openalex.org/I4210144665","display_name":"University of O'Higgins","ror":"https://ror.org/044cse639","country_code":"CL","type":"education","lineage":["https://openalex.org/I4210144665"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Pedro P\u00e9rez-Aros","raw_affiliation_strings":["Instituto de Ciencias de la Ingeniera, Universidad de O\u2019Higgins, Rancagua, Chile","Instituto de Ciencias de la Ingeniera, Universidad de O'Higgins, Rancagua, Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Ciencias de la Ingeniera, Universidad de O\u2019Higgins, Rancagua, Chile","institution_ids":["https://openalex.org/I4210144665"]},{"raw_affiliation_string":"Instituto de Ciencias de la Ingeniera, Universidad de O'Higgins, Rancagua, Chile","institution_ids":["https://openalex.org/I4210144665"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5080745391"],"corresponding_institution_ids":["https://openalex.org/I4210143116"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":1.62,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.84003591,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"185","issue":"1","first_page":"239","last_page":"269"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9987999796867371,"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":0.9987999796867371,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9926000237464905,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9886000156402588,"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/differentiable-function","display_name":"Differentiable function","score":0.8653767108917236},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7381357550621033},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.573188304901123},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5664349794387817},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.5507904887199402},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5426254272460938},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5128874778747559},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.512330174446106},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45907163619995117},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.4418851435184479},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.43377885222435},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4232960045337677},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20339709520339966},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14624780416488647}],"concepts":[{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.8653767108917236},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7381357550621033},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.573188304901123},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5664349794387817},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.5507904887199402},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5426254272460938},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5128874778747559},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.512330174446106},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45907163619995117},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.4418851435184479},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.43377885222435},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4232960045337677},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20339709520339966},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14624780416488647},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-020-01634-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-020-01634-9","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:joptap:v:185:y:2020:i:1:d:10.1007_s10957-020-01634-9","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-020-01634-9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6468594566","display_name":null,"funder_award_id":"Fondecyt Regular 1190110","funder_id":"https://openalex.org/F4320325593","funder_display_name":"Consejo Nacional de Innovaci\u00f3n, Ciencia y Tecnolog\u00eda"}],"funders":[{"id":"https://openalex.org/F4320325593","display_name":"Consejo Nacional de Innovaci\u00f3n, Ciencia y Tecnolog\u00eda","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1559197676","https://openalex.org/W1619636526","https://openalex.org/W1862288364","https://openalex.org/W1979512503","https://openalex.org/W1989631052","https://openalex.org/W2022808402","https://openalex.org/W2029225872","https://openalex.org/W2036529462","https://openalex.org/W2053391173","https://openalex.org/W2055088712","https://openalex.org/W2055661359","https://openalex.org/W2090905570","https://openalex.org/W2090967418","https://openalex.org/W2093304942","https://openalex.org/W2102379475","https://openalex.org/W2105378603","https://openalex.org/W2118382239","https://openalex.org/W2122861691","https://openalex.org/W2127294592","https://openalex.org/W2142261996","https://openalex.org/W2261073569","https://openalex.org/W2500225789","https://openalex.org/W2529781235","https://openalex.org/W2569380384","https://openalex.org/W2616886504","https://openalex.org/W2622903347","https://openalex.org/W2751459826","https://openalex.org/W2763608097","https://openalex.org/W2764133341","https://openalex.org/W2798344481","https://openalex.org/W2808856084","https://openalex.org/W2885962488","https://openalex.org/W2951762099","https://openalex.org/W3106992008","https://openalex.org/W4245807314","https://openalex.org/W4249513058","https://openalex.org/W4253577938","https://openalex.org/W4300246981"],"related_works":["https://openalex.org/W4385382439","https://openalex.org/W2387241522","https://openalex.org/W4206704743","https://openalex.org/W2088344732","https://openalex.org/W4312674943","https://openalex.org/W4245653589","https://openalex.org/W2327930114","https://openalex.org/W2390817143","https://openalex.org/W436931041","https://openalex.org/W2894731288"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
