{"id":"https://openalex.org/W2776611667","doi":"https://doi.org/10.1007/s10957-017-1209-x","title":"Necessary and Sufficient Conditions for Strong Fenchel\u2013Lagrange Duality via a Coupling Conjugation Scheme","display_name":"Necessary and Sufficient Conditions for Strong Fenchel\u2013Lagrange Duality via a Coupling Conjugation Scheme","publication_year":2017,"publication_date":"2017-12-19","ids":{"openalex":"https://openalex.org/W2776611667","doi":"https://doi.org/10.1007/s10957-017-1209-x","mag":"2776611667"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-017-1209-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-017-1209-x","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/A5051675554","display_name":"M. D. Fajardo","orcid":"https://orcid.org/0000-0001-8405-7589"},"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"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"M. D. Fajardo","raw_affiliation_strings":["University of Alicante, Alicante, Spain"],"raw_orcid":"https://orcid.org/0000-0001-8405-7589","affiliations":[{"raw_affiliation_string":"University of Alicante, Alicante, Spain","institution_ids":["https://openalex.org/I130194489"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028553424","display_name":"Jos\u00e9 Vidal-N\u00fa\u00f1ez","orcid":"https://orcid.org/0000-0002-1190-6700"},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"J. Vidal","raw_affiliation_strings":["Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5051675554"],"corresponding_institution_ids":["https://openalex.org/I130194489"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.659,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.86225465,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"176","issue":"1","first_page":"57","last_page":"73"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9958000183105469,"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":0.9958000183105469,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9919999837875366,"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"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9890999794006348,"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/duality","display_name":"Duality (order theory)","score":0.8288226127624512},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8031970262527466},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.7312595248222351},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.6676051616668701},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6299953460693359},{"id":"https://openalex.org/keywords/duality-gap","display_name":"Duality gap","score":0.627496600151062},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5746141672134399},{"id":"https://openalex.org/keywords/wolfe-duality","display_name":"Wolfe duality","score":0.5667895674705505},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.5435833930969238},{"id":"https://openalex.org/keywords/weak-duality","display_name":"Weak duality","score":0.5322275757789612},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.48578694462776184},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.4846859276294708},{"id":"https://openalex.org/keywords/fenchels-duality-theorem","display_name":"Fenchel's duality theorem","score":0.47841960191726685},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.463803768157959},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41299569606781006},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39859870076179504},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30074697732925415},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24012824892997742},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.17696130275726318},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05182087421417236}],"concepts":[{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.8288226127624512},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8031970262527466},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.7312595248222351},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.6676051616668701},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6299953460693359},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.627496600151062},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5746141672134399},{"id":"https://openalex.org/C109456813","wikidata":"https://www.wikidata.org/wiki/Q8029991","display_name":"Wolfe duality","level":5,"score":0.5667895674705505},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.5435833930969238},{"id":"https://openalex.org/C80682859","wikidata":"https://www.wikidata.org/wiki/Q7977943","display_name":"Weak duality","level":4,"score":0.5322275757789612},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.48578694462776184},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.4846859276294708},{"id":"https://openalex.org/C32580822","wikidata":"https://www.wikidata.org/wiki/Q5443003","display_name":"Fenchel's duality theorem","level":5,"score":0.47841960191726685},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.463803768157959},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41299569606781006},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39859870076179504},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30074697732925415},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24012824892997742},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.17696130275726318},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05182087421417236},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10957-017-1209-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-017-1209-x","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:176:y:2018:i:1:d:10.1007_s10957-017-1209-x","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-017-1209-x","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"},{"id":"pmh:oai:rua.ua.es:10045/73201","is_oa":false,"landing_page_url":"http://hdl.handle.net/10045/73201","pdf_url":null,"source":{"id":"https://openalex.org/S4306400416","display_name":"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":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4699999988079071}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321864","display_name":"Generalitat Valenciana","ror":"https://ror.org/0097mvx21"},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W197071561","https://openalex.org/W341071838","https://openalex.org/W1653619892","https://openalex.org/W1966580598","https://openalex.org/W1979971434","https://openalex.org/W1984605028","https://openalex.org/W1993247264","https://openalex.org/W2016306996","https://openalex.org/W2028766715","https://openalex.org/W2029473142","https://openalex.org/W2048540358","https://openalex.org/W2063620298","https://openalex.org/W2064880458","https://openalex.org/W2071802567","https://openalex.org/W2085138249","https://openalex.org/W2092061595","https://openalex.org/W2195547081","https://openalex.org/W2213495066","https://openalex.org/W2321986352","https://openalex.org/W2325192077","https://openalex.org/W2519376024","https://openalex.org/W2598061374","https://openalex.org/W2726664478","https://openalex.org/W3129885716","https://openalex.org/W4206412600","https://openalex.org/W4293820388"],"related_works":["https://openalex.org/W4220928172","https://openalex.org/W3213165575","https://openalex.org/W2029896594","https://openalex.org/W2366010475","https://openalex.org/W2423508375","https://openalex.org/W1994149084","https://openalex.org/W2105158595","https://openalex.org/W2016306996","https://openalex.org/W2080388204","https://openalex.org/W2073406242"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
