{"id":"https://openalex.org/W2086286431","doi":"https://doi.org/10.1007/s10898-009-9486-z","title":"Duality and optimality conditions for generalized equilibrium problems involving DC functions","display_name":"Duality and optimality conditions for generalized equilibrium problems involving DC functions","publication_year":2009,"publication_date":"2009-11-07","ids":{"openalex":"https://openalex.org/W2086286431","doi":"https://doi.org/10.1007/s10898-009-9486-z","mag":"2086286431"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-009-9486-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-009-9486-z","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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 Global 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/A5101466845","display_name":"N. Dinh","orcid":"https://orcid.org/0000-0001-6558-1289"},"institutions":[{"id":"https://openalex.org/I123565023","display_name":"Vietnam National University Ho Chi Minh City","ror":"https://ror.org/00waaqh38","country_code":"VN","type":"education","lineage":["https://openalex.org/I123565023"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"N. Dinh","raw_affiliation_strings":["Department of Mathematics, International University, Vietnam National University, Ho Chi Minh City, Vietnam"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, International University, Vietnam National University, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I123565023"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077911889","display_name":"Jean Jacques Strodiot","orcid":null},"institutions":[{"id":"https://openalex.org/I149768937","display_name":"University of Namur","ror":"https://ror.org/03d1maw17","country_code":"BE","type":"education","lineage":["https://openalex.org/I149768937"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"J. J. Strodiot","raw_affiliation_strings":["Department of Mathematics, University of Namur (FUNDP), Namur, Belgium","[Department of Mathematics, University of Namur-FUNDP, Namur, Belgium]"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Namur (FUNDP), Namur, Belgium","institution_ids":["https://openalex.org/I149768937"]},{"raw_affiliation_string":"[Department of Mathematics, University of Namur-FUNDP, Namur, Belgium]","institution_ids":["https://openalex.org/I149768937"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015905629","display_name":"Van Hien Nguyen","orcid":"https://orcid.org/0000-0002-5665-4981"},"institutions":[{"id":"https://openalex.org/I149768937","display_name":"University of Namur","ror":"https://ror.org/03d1maw17","country_code":"BE","type":"education","lineage":["https://openalex.org/I149768937"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"V. H. Nguyen","raw_affiliation_strings":["Department of Mathematics, University of Namur (FUNDP), Namur, Belgium","[Department of Mathematics, University of Namur-FUNDP, Namur, Belgium]"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Namur (FUNDP), Namur, Belgium","institution_ids":["https://openalex.org/I149768937"]},{"raw_affiliation_string":"[Department of Mathematics, University of Namur-FUNDP, Namur, Belgium]","institution_ids":["https://openalex.org/I149768937"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101466845"],"corresponding_institution_ids":["https://openalex.org/I123565023"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":null,"fwci":2.1142,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.8702375,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"48","issue":"2","first_page":"183","last_page":"208"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9983999729156494,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.968999981880188,"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/mathematics","display_name":"Mathematics","score":0.8524882793426514},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.7668180465698242},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.6599746942520142},{"id":"https://openalex.org/keywords/duality-gap","display_name":"Duality gap","score":0.5944666862487793},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.5415435433387756},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.49565064907073975},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.49404340982437134},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.48954686522483826},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.48486337065696716},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4631611108779907},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4584774971008301},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4530562460422516},{"id":"https://openalex.org/keywords/wolfe-duality","display_name":"Wolfe duality","score":0.4449279308319092},{"id":"https://openalex.org/keywords/weak-duality","display_name":"Weak duality","score":0.42626330256462097},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.42526325583457947},{"id":"https://openalex.org/keywords/perturbation-function","display_name":"Perturbation function","score":0.42481905221939087},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4197290241718292},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.31010037660598755},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3016904592514038},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0892907977104187}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8524882793426514},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.7668180465698242},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.6599746942520142},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.5944666862487793},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.5415435433387756},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.49565064907073975},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.49404340982437134},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.48954686522483826},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.48486337065696716},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4631611108779907},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4584774971008301},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4530562460422516},{"id":"https://openalex.org/C109456813","wikidata":"https://www.wikidata.org/wiki/Q8029991","display_name":"Wolfe duality","level":5,"score":0.4449279308319092},{"id":"https://openalex.org/C80682859","wikidata":"https://www.wikidata.org/wiki/Q7977943","display_name":"Weak duality","level":4,"score":0.42626330256462097},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.42526325583457947},{"id":"https://openalex.org/C102144036","wikidata":"https://www.wikidata.org/wiki/Q7170952","display_name":"Perturbation function","level":5,"score":0.42481905221939087},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4197290241718292},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31010037660598755},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3016904592514038},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0892907977104187},{"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":4,"locations":[{"id":"doi:10.1007/s10898-009-9486-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-009-9486-z","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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 Global Optimization","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:jglopt:v:48:y:2010:i:2:p:183-208","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s10898-009-9486-z","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:dial.uclouvain.be:boreal:98111","is_oa":false,"landing_page_url":"http://hdl.handle.net/2078.2/98111","pdf_url":null,"source":{"id":"https://openalex.org/S4306401974","display_name":"DIAL (Catholic University of Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Global Optimization : an international journal dealing with theoretical and computational aspects of seeking global optima and their applications in science, management, and engineering, Vol. 48, no. 2, p. 183-208 (2010)","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.unamur.be:openaire_cris_publications/8bd9d53f-f532-4b09-92ea-c78dace65d18","is_oa":false,"landing_page_url":"https://researchportal.unamur.be/en/publications/8bd9d53f-f532-4b09-92ea-c78dace65d18","pdf_url":null,"source":{"id":"https://openalex.org/S4406922457","display_name":"Repository of the University of Namur","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Dinh , N , Strodiot , J-J & Nguyen , V H 2009 , Duality and optimality conditions for generalized equilibrium problems involving DC functions . FUNDP, Facult\u00e9 des Sciences. D\u00e9partement de Math\u00e9matique. , Namur .","raw_type":"book"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320335302","display_name":"Universit\u00e9 de Namur","ror":"https://ror.org/03d1maw17"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W152555402","https://openalex.org/W574400632","https://openalex.org/W654824284","https://openalex.org/W1549597154","https://openalex.org/W1556141937","https://openalex.org/W1963909982","https://openalex.org/W1968747019","https://openalex.org/W1981414252","https://openalex.org/W1988833018","https://openalex.org/W1989313814","https://openalex.org/W2006581042","https://openalex.org/W2014211093","https://openalex.org/W2021295607","https://openalex.org/W2041363761","https://openalex.org/W2045731584","https://openalex.org/W2055572834","https://openalex.org/W2062868300","https://openalex.org/W2073718458","https://openalex.org/W2083187551","https://openalex.org/W2114605231","https://openalex.org/W2136553956","https://openalex.org/W2147101399","https://openalex.org/W2165543081","https://openalex.org/W2175532135","https://openalex.org/W2287679767"],"related_works":["https://openalex.org/W2103632601","https://openalex.org/W2241982889","https://openalex.org/W2201555914","https://openalex.org/W2016306996","https://openalex.org/W1985466396","https://openalex.org/W2325192077","https://openalex.org/W3125561280","https://openalex.org/W2963183154","https://openalex.org/W2076232126","https://openalex.org/W2086286431"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}