{"id":"https://openalex.org/W3103348010","doi":"https://doi.org/10.1007/s10107-020-01597-9","title":"A unified concept of approximate and quasi efficient solutions and associated subdifferentials in multiobjective optimization","display_name":"A unified concept of approximate and quasi efficient solutions and associated subdifferentials in multiobjective optimization","publication_year":2020,"publication_date":"2020-11-18","ids":{"openalex":"https://openalex.org/W3103348010","doi":"https://doi.org/10.1007/s10107-020-01597-9","mag":"3103348010"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-020-01597-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-020-01597-9","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://e-spacio.uned.es/bitstreams/0e85a4ce-5873-4397-a6a5-3c9f0e861b28/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016969187","display_name":"L. Huerga","orcid":"https://orcid.org/0000-0002-6634-3482"},"institutions":[{"id":"https://openalex.org/I178450904","display_name":"Universidad Nacional de Educaci\u00f3n a Distancia","ror":"https://ror.org/02msb5n36","country_code":"ES","type":"education","lineage":["https://openalex.org/I178450904"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"L. Huerga","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educaci\u00f3n a Distancia (UNED), Calle Juan del Rosal, 12, 28040, Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0002-6634-3482","affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educaci\u00f3n a Distancia (UNED), Calle Juan del Rosal, 12, 28040, Madrid, Spain","institution_ids":["https://openalex.org/I178450904"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069972821","display_name":"Bienvenido Jim\u00e9nez","orcid":"https://orcid.org/0000-0003-1513-8590"},"institutions":[{"id":"https://openalex.org/I178450904","display_name":"Universidad Nacional de Educaci\u00f3n a Distancia","ror":"https://ror.org/02msb5n36","country_code":"ES","type":"education","lineage":["https://openalex.org/I178450904"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"B. Jim\u00e9nez","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educaci\u00f3n a Distancia (UNED), Calle Juan del Rosal, 12, 28040, Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0003-1513-8590","affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educaci\u00f3n a Distancia (UNED), Calle Juan del Rosal, 12, 28040, Madrid, Spain","institution_ids":["https://openalex.org/I178450904"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011329543","display_name":"Dinh The Luc","orcid":"https://orcid.org/0000-0003-1076-404X"},"institutions":[{"id":"https://openalex.org/I141445968","display_name":"Ton Duc Thang University","ror":"https://ror.org/01drq0835","country_code":"VN","type":"education","lineage":["https://openalex.org/I141445968"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"D. T. Luc","raw_affiliation_strings":["Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam","Parametric MultiObjective Optimization Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam"],"raw_orcid":"https://orcid.org/0000-0003-1076-404X","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I141445968"]},{"raw_affiliation_string":"Parametric MultiObjective Optimization Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I141445968"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001299859","display_name":"Vicente Novo","orcid":"https://orcid.org/0000-0001-9033-3180"},"institutions":[{"id":"https://openalex.org/I178450904","display_name":"Universidad Nacional de Educaci\u00f3n a Distancia","ror":"https://ror.org/02msb5n36","country_code":"ES","type":"education","lineage":["https://openalex.org/I178450904"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"V. Novo","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educaci\u00f3n a Distancia (UNED), Calle Juan del Rosal, 12, 28040, Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0001-9033-3180","affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educaci\u00f3n a Distancia (UNED), Calle Juan del Rosal, 12, 28040, Madrid, Spain","institution_ids":["https://openalex.org/I178450904"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001299859"],"corresponding_institution_ids":["https://openalex.org/I178450904"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":0.5065,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.72539374,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"189","issue":"1-2","first_page":"379","last_page":"407"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9962000250816345,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9871000051498413,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.898561954498291},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7892779111862183},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6464083194732666},{"id":"https://openalex.org/keywords/vector-optimization","display_name":"Vector optimization","score":0.462654173374176},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4599302411079407},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4599120020866394},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.44736433029174805},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.22808077931404114},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.1650715470314026},{"id":"https://openalex.org/keywords/multi-swarm-optimization","display_name":"Multi-swarm optimization","score":0.06726604700088501},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.062060773372650146}],"concepts":[{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.898561954498291},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7892779111862183},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6464083194732666},{"id":"https://openalex.org/C164088818","wikidata":"https://www.wikidata.org/wiki/Q7917833","display_name":"Vector optimization","level":4,"score":0.462654173374176},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4599302411079407},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4599120020866394},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.44736433029174805},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.22808077931404114},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.1650715470314026},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.06726604700088501},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.062060773372650146},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10107-020-01597-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-020-01597-9","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:e-spacio.uned.es:20.500.14468/12544","is_oa":true,"landing_page_url":"https://hdl.handle.net/20.500.14468/12544","pdf_url":"https://e-spacio.uned.es/bitstreams/0e85a4ce-5873-4397-a6a5-3c9f0e861b28/download","source":{"id":"https://openalex.org/S7407055166","display_name":"UNED repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"journal article"}],"best_oa_location":{"id":"pmh:oai:e-spacio.uned.es:20.500.14468/12544","is_oa":true,"landing_page_url":"https://hdl.handle.net/20.500.14468/12544","pdf_url":"https://e-spacio.uned.es/bitstreams/0e85a4ce-5873-4397-a6a5-3c9f0e861b28/download","source":{"id":"https://openalex.org/S7407055166","display_name":"UNED repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"journal article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G565534154","display_name":null,"funder_award_id":"PGC2018-096899-B-I00","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G6728930308","display_name":null,"funder_award_id":"PGC 2018","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G6731467812","display_name":null,"funder_award_id":"PGC2018","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G7384923209","display_name":null,"funder_award_id":"PGC2018-096899-B-I00","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"}],"funders":[{"id":"https://openalex.org/F4320315062","display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","ror":null},{"id":"https://openalex.org/F4320323261","display_name":"Universidad Nacional de Educaci\u00f3n a Distancia","ror":"https://ror.org/02msb5n36"},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3103348010.pdf","grobid_xml":"https://content.openalex.org/works/W3103348010.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W4394890","https://openalex.org/W113278869","https://openalex.org/W187778025","https://openalex.org/W398727469","https://openalex.org/W632378324","https://openalex.org/W1554939947","https://openalex.org/W1582299569","https://openalex.org/W1585268704","https://openalex.org/W1971296668","https://openalex.org/W1974018779","https://openalex.org/W1975805250","https://openalex.org/W1977750299","https://openalex.org/W1983742072","https://openalex.org/W1990923130","https://openalex.org/W1993708577","https://openalex.org/W2000904165","https://openalex.org/W2005341901","https://openalex.org/W2014211093","https://openalex.org/W2036474185","https://openalex.org/W2037534711","https://openalex.org/W2039887265","https://openalex.org/W2043023177","https://openalex.org/W2061942560","https://openalex.org/W2067243588","https://openalex.org/W2072307957","https://openalex.org/W2072886676","https://openalex.org/W2074909374","https://openalex.org/W2076820840","https://openalex.org/W2110829390","https://openalex.org/W2154456062","https://openalex.org/W2201384637","https://openalex.org/W2478963760","https://openalex.org/W2592202507","https://openalex.org/W2781583626","https://openalex.org/W2802620382","https://openalex.org/W2937299879","https://openalex.org/W4231758816","https://openalex.org/W4249125060","https://openalex.org/W4249667877"],"related_works":["https://openalex.org/W2565276936","https://openalex.org/W2766340440","https://openalex.org/W4385713703","https://openalex.org/W3110411377","https://openalex.org/W4308905590","https://openalex.org/W2040739535","https://openalex.org/W2388375429","https://openalex.org/W2381571088","https://openalex.org/W109016340","https://openalex.org/W1992731528"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}
