{"id":"https://openalex.org/W3135705422","doi":"https://doi.org/10.1137/19m1303320","title":"Necessary and Sufficient Optimality Conditions in DC Semi-infinite Programming","display_name":"Necessary and Sufficient Optimality Conditions in DC Semi-infinite Programming","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3135705422","doi":"https://doi.org/10.1137/19m1303320","mag":"3135705422"},"language":"en","primary_location":{"id":"doi:10.1137/19m1303320","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1303320","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://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/176607","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101509519","display_name":"Rafael Corr\u00eaa","orcid":"https://orcid.org/0000-0002-8112-4683"},"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":true,"raw_author_name":"Rafael Correa","raw_affiliation_strings":["Universidad de O'Higgins"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad de O'Higgins","institution_ids":["https://openalex.org/I4210144665"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100715600","display_name":"Marco A. L\u00f3pez","orcid":"https://orcid.org/0000-0002-0619-9618"},"institutions":[{"id":"https://openalex.org/I130194489","display_name":"University of Alicante","ror":"https://ror.org/05t8bcz72","country_code":"ES","type":"education","lineage":["https://openalex.org/I130194489"]},{"id":"https://openalex.org/I149672521","display_name":"Federation University","ror":"https://ror.org/05qbzwv83","country_code":"AU","type":"education","lineage":["https://openalex.org/I149672521"]}],"countries":["AU","ES"],"is_corresponding":false,"raw_author_name":"M. A. L\u00f3pez","raw_affiliation_strings":["Federa-tion University, Australia","Department of Mathematics, University of Alicante, Alicante 03080, Spain, and CIAO,"],"raw_orcid":"https://orcid.org/0000-0002-0619-9618","affiliations":[{"raw_affiliation_string":"Federa-tion University, Australia","institution_ids":["https://openalex.org/I149672521"]},{"raw_affiliation_string":"Department of Mathematics, University of Alicante, Alicante 03080, Spain, and CIAO,","institution_ids":["https://openalex.org/I130194489"]}]},{"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 Ingenier\u00eda, Universidad de O'Higgins, Rancagua 2820000, Chile"],"raw_orcid":"https://orcid.org/0000-0002-8756-3011","affiliations":[{"raw_affiliation_string":"Instituto de Ciencias de la Ingenier\u00eda, Universidad de O'Higgins, Rancagua 2820000, Chile","institution_ids":["https://openalex.org/I4210144665"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101509519"],"corresponding_institution_ids":["https://openalex.org/I4210144665"],"apc_list":null,"apc_paid":null,"fwci":1.4517,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.83656369,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"31","issue":"1","first_page":"837","last_page":"865"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9994999766349792,"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":0.9994999766349792,"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":0.995199978351593,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.9750000238418579,"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":0.8044683933258057},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.6830712556838989},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6816174983978271},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5204606056213379},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.49010810256004333},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.481598824262619},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.46033674478530884},{"id":"https://openalex.org/keywords/conic-optimization","display_name":"Conic optimization","score":0.43621882796287537},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4242519438266754},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.41834598779678345},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.2917659878730774}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8044683933258057},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.6830712556838989},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6816174983978271},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5204606056213379},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.49010810256004333},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.481598824262619},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.46033674478530884},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.43621882796287537},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4242519438266754},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.41834598779678345},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.2917659878730774},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/19m1303320","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1303320","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:vital:15142","is_oa":true,"landing_page_url":"http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/176607","pdf_url":"http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/176607","source":{"id":"https://openalex.org/S4306400234","display_name":"FedUni ResearchOnline (Federation University Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210158496","host_organization_name":"Australian Federation of University Women \u2013 South Australia","host_organization_lineage":["https://openalex.org/I4210158496"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:rua.ua.es:10045/114450","is_oa":false,"landing_page_url":"http://hdl.handle.net/10045/114450","pdf_url":null,"source":{"id":"https://openalex.org/S4306400975","display_name":"RUA, Repositorio Institucional de la Universidad de Alicante (Universidad de Alicante)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130194489","host_organization_name":"University of Alicante","host_organization_lineage":["https://openalex.org/I130194489"],"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:vital:15142","is_oa":true,"landing_page_url":"http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/176607","pdf_url":"http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/176607","source":{"id":"https://openalex.org/S4306400234","display_name":"FedUni ResearchOnline (Federation University Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210158496","host_organization_name":"Australian Federation of University Women \u2013 South Australia","host_organization_lineage":["https://openalex.org/I4210158496"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2024898639","display_name":"GENERALIZED DIFFERENTIATION AND VARIATIONAL ANALYSIS OF PROBABILITY FUNCTIONS","funder_award_id":"1200283","funder_id":"https://openalex.org/F4320331146","funder_display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo"},{"id":"https://openalex.org/G2109352133","display_name":null,"funder_award_id":"PGC2018-097960-B-C21","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G3704643367","display_name":"STOCHASTIC OPTIMIZATION AND CHANCE CONSTRAINTS WITH APPLICATIONS TO ENERGY","funder_award_id":"MATH190003","funder_id":"https://openalex.org/F4320331146","funder_display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo"},{"id":"https://openalex.org/G4786324315","display_name":null,"funder_award_id":"1200283","funder_id":"https://openalex.org/F4320338073","funder_display_name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico"},{"id":"https://openalex.org/G490073602","display_name":null,"funder_award_id":"PGC2018","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G538444432","display_name":null,"funder_award_id":"PGC2018-097960-B-C21","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G7845768852","display_name":null,"funder_award_id":"Fondecyt Regular 1190110","funder_id":"https://openalex.org/F4320331146","funder_display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo"},{"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"},{"id":"https://openalex.org/G8585180605","display_name":"SUBDIFFERENTIAL CALCULUS IN THE FRAMEWORK OF DC FUNCTIONS AND APPLICATIONS","funder_award_id":"1190110","funder_id":"https://openalex.org/F4320331146","funder_display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo"},{"id":"https://openalex.org/G8957832040","display_name":null,"funder_award_id":"DP 180100602","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320315062","display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","ror":null},{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320323458","display_name":"Universidad de Chile","ror":"https://ror.org/047gc3g35"},{"id":"https://openalex.org/F4320331146","display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo","ror":null},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"},{"id":"https://openalex.org/F4320338073","display_name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico","ror":"https://ror.org/02ap3w078"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3135705422.pdf"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W81972919","https://openalex.org/W1986606318","https://openalex.org/W1988833018","https://openalex.org/W1993613781","https://openalex.org/W1998611061","https://openalex.org/W2014211093","https://openalex.org/W2037005512","https://openalex.org/W2042562476","https://openalex.org/W2046981034","https://openalex.org/W2069374819","https://openalex.org/W2103372919","https://openalex.org/W2129048736","https://openalex.org/W2136553956","https://openalex.org/W2474080880","https://openalex.org/W2536563272","https://openalex.org/W2804571214","https://openalex.org/W2914166403","https://openalex.org/W2924141044","https://openalex.org/W2940209886","https://openalex.org/W2962921834","https://openalex.org/W2963756474","https://openalex.org/W2968746229"],"related_works":["https://openalex.org/W4381623700","https://openalex.org/W2317735557","https://openalex.org/W2126351339","https://openalex.org/W4394888055","https://openalex.org/W4297174051","https://openalex.org/W608274465","https://openalex.org/W2012204533","https://openalex.org/W2216036554","https://openalex.org/W3139158759","https://openalex.org/W2275184629"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3],"particular":[4],"families":[5,44],"of":[6,12,21,24,32,45,53],"DC":[7,46,74,78,90],"optimization":[8,47],"problems":[9,33,48,93],"involving":[10],"suprema":[11],"convex":[13],"functions.":[14],"We":[15],"show":[16],"that":[17],"the":[18,97],"specific":[19],"structure":[20],"this":[22],"type":[23],"function":[25],"allows":[26],"us":[27],"to":[28,89],"cover":[29],"a":[30,86],"variety":[31],"in":[34,73,96],"nonconvex":[35],"programming.":[36],"Necessary":[37],"and":[38,65,70,77],"sufficient":[39,66],"optimality":[40,72],"conditions":[41,67],"for":[42,68],"these":[43,54],"are":[49,57],"established,":[50],"where":[51],"some":[52],"structural":[55],"features":[56],"conveniently":[58],"exploited.":[59],"More":[60],"precisely,":[61],"we":[62],"derive":[63],"necessary":[64],"(global":[69],"local)":[71],"semi-infinite":[75],"programming":[76,92],"cone-constrained":[79],"optimization,":[80],"under":[81],"natural":[82],"constraint":[83],"qualifications.":[84],"Finally,":[85],"penalty":[87],"approach":[88],"abstract":[91],"is":[94],"developed":[95],"last":[98],"section.":[99]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-27T08:26:11.824852","created_date":"2025-10-10T00:00:00"}
