{"id":"https://openalex.org/W1966946241","doi":"https://doi.org/10.1007/s10898-012-9983-3","title":"Versions of Ekeland\u2019s variational principle involving set perturbations","display_name":"Versions of Ekeland\u2019s variational principle involving set perturbations","publication_year":2012,"publication_date":"2012-09-18","ids":{"openalex":"https://openalex.org/W1966946241","doi":"https://doi.org/10.1007/s10898-012-9983-3","mag":"1966946241"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-012-9983-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-012-9983-3","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/A5059731357","display_name":"Phan Qu\u1ed1c Kh\u00e1nh","orcid":"https://orcid.org/0000-0002-0524-0498"},"institutions":[{"id":"https://openalex.org/I883909435","display_name":"International University","ror":"https://ror.org/02knr1992","country_code":"KH","type":"education","lineage":["https://openalex.org/I883909435"]},{"id":"https://openalex.org/I228151691","display_name":"Ho Chi Minh City International University","ror":"https://ror.org/003szmg30","country_code":"VN","type":"education","lineage":["https://openalex.org/I123565023","https://openalex.org/I228151691"]}],"countries":["KH","VN"],"is_corresponding":true,"raw_author_name":"Phan Quoc Khanh","raw_affiliation_strings":["Department of Mathematics, International University of Hochiminh City, Linh Trung, Thu Duc, Hochiminh City, Vietnam","International University of Hochiminh City"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, International University of Hochiminh City, Linh Trung, Thu Duc, Hochiminh City, Vietnam","institution_ids":["https://openalex.org/I228151691"]},{"raw_affiliation_string":"International University of Hochiminh City","institution_ids":["https://openalex.org/I883909435"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046587499","display_name":"\u0110inh Ng\u1ecdc Qu\u00fd","orcid":null},"institutions":[{"id":"https://openalex.org/I177733328","display_name":"Can Tho University","ror":"https://ror.org/0071qz696","country_code":"VN","type":"education","lineage":["https://openalex.org/I177733328"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Dinh Ngoc Quy","raw_affiliation_strings":["Department of Mathematics, Cantho University, Cantho, Vietnam","Cantho University"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Cantho University, Cantho, Vietnam","institution_ids":["https://openalex.org/I177733328"]},{"raw_affiliation_string":"Cantho University","institution_ids":["https://openalex.org/I177733328"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5059731357"],"corresponding_institution_ids":["https://openalex.org/I228151691","https://openalex.org/I883909435"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":null,"fwci":2.106,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.84481328,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"57","issue":"3","first_page":"951","last_page":"968"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9970999956130981,"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"}},"topics":[{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9970999956130981,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9970999956130981,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9969000220298767,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8912019729614258},{"id":"https://openalex.org/keywords/variational-principle","display_name":"Variational principle","score":0.716431736946106},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.5683914422988892},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5325143933296204},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4648970663547516},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.46399566531181335},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40680697560310364},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3806721866130829},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37955421209335327},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16053494811058044},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15430766344070435},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05996072292327881}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8912019729614258},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.716431736946106},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.5683914422988892},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5325143933296204},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4648970663547516},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.46399566531181335},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40680697560310364},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3806721866130829},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37955421209335327},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16053494811058044},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15430766344070435},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05996072292327881},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10898-012-9983-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-012-9983-3","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:57:y:2013:i:3:p:951-968","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s10898-012-9983-3","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":[{"score":0.7300000190734863,"display_name":"Climate action","id":"https://metadata.un.org/sdg/13"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320309617","display_name":"National Foundation for Science and Technology Development","ror":"https://ror.org/04rw64z44"},{"id":"https://openalex.org/F4320324338","display_name":"Vietnam Institute for Advanced Study in Mathematics","ror":"https://ror.org/00jn6x547"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W117217602","https://openalex.org/W417516028","https://openalex.org/W1542300426","https://openalex.org/W1582299569","https://openalex.org/W1977750299","https://openalex.org/W1981896023","https://openalex.org/W1993071711","https://openalex.org/W1995700855","https://openalex.org/W1997201451","https://openalex.org/W1998057492","https://openalex.org/W2003663149","https://openalex.org/W2013118573","https://openalex.org/W2018127805","https://openalex.org/W2037227885","https://openalex.org/W2037534711","https://openalex.org/W2048840404","https://openalex.org/W2065765809","https://openalex.org/W2065840522","https://openalex.org/W2067146610","https://openalex.org/W2083978795","https://openalex.org/W2084726813","https://openalex.org/W2086124327","https://openalex.org/W2092651824","https://openalex.org/W2138278189","https://openalex.org/W2484712261","https://openalex.org/W2594483763","https://openalex.org/W6722028504"],"related_works":["https://openalex.org/W2371409811","https://openalex.org/W4253179511","https://openalex.org/W2956921597","https://openalex.org/W2070412032","https://openalex.org/W4250430376","https://openalex.org/W4249185839","https://openalex.org/W2116371063","https://openalex.org/W2888047994","https://openalex.org/W2383812375","https://openalex.org/W4299852727"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}