{"id":"https://openalex.org/W2037227885","doi":"https://doi.org/10.1007/s001860050020","title":"Ekeland's \u03b5-variational principle for set-valued mappings","display_name":"Ekeland's \u03b5-variational principle for set-valued mappings","publication_year":1998,"publication_date":"1998-11-01","ids":{"openalex":"https://openalex.org/W2037227885","doi":"https://doi.org/10.1007/s001860050020","mag":"2037227885"},"language":"en","primary_location":{"id":"doi:10.1007/s001860050020","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s001860050020","pdf_url":null,"source":{"id":"https://openalex.org/S126160977","display_name":"Mathematical Methods of Operations Research","issn_l":"1432-2994","issn":["1432-2994","1432-5217"],"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 Methods of Operations Research","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/A5048783624","display_name":"Guang Ya Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I84653119","display_name":"Academia Sinica","ror":"https://ror.org/05bxb3784","country_code":"TW","type":"facility","lineage":["https://openalex.org/I84653119"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN","TW"],"is_corresponding":true,"raw_author_name":"Guang Ya Chen","raw_affiliation_strings":["Institute of Systems Science, Academia Sinica, Beijing 100080, China, , , , , , CN","Institute of Systems Science, Academia Sinica, Beijing 100080, China, CN"],"affiliations":[{"raw_affiliation_string":"Institute of Systems Science, Academia Sinica, Beijing 100080, China, , , , , , CN","institution_ids":["https://openalex.org/I4210120485"]},{"raw_affiliation_string":"Institute of Systems Science, Academia Sinica, Beijing 100080, China, CN","institution_ids":["https://openalex.org/I84653119"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028578315","display_name":"Xiaoxu Huang","orcid":"https://orcid.org/0000-0002-4635-6112"},"institutions":[{"id":"https://openalex.org/I84653119","display_name":"Academia Sinica","ror":"https://ror.org/05bxb3784","country_code":"TW","type":"facility","lineage":["https://openalex.org/I84653119"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN","TW"],"is_corresponding":false,"raw_author_name":"X. X. Huang","raw_affiliation_strings":["Institute of Systems Science, Academia Sinica, Beijing 100080, China, , , , , , CN","Institute of Systems Science, Academia Sinica, Beijing 100080, China, CN"],"affiliations":[{"raw_affiliation_string":"Institute of Systems Science, Academia Sinica, Beijing 100080, China, , , , , , CN","institution_ids":["https://openalex.org/I4210120485"]},{"raw_affiliation_string":"Institute of Systems Science, Academia Sinica, Beijing 100080, China, CN","institution_ids":["https://openalex.org/I84653119"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5048783624"],"corresponding_institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I84653119"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.0202,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.76038367,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"48","issue":"2","first_page":"181","last_page":"186"},"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":0.961899995803833,"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":0.9487000107765198,"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/mathematics","display_name":"Mathematics","score":0.783734142780304},{"id":"https://openalex.org/keywords/variational-principle","display_name":"Variational principle","score":0.7757574915885925},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6663835644721985},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5270405411720276},{"id":"https://openalex.org/keywords/variational-analysis","display_name":"Variational analysis","score":0.49106669425964355},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36684244871139526},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25577491521835327},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16815689206123352}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.783734142780304},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.7757574915885925},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6663835644721985},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5270405411720276},{"id":"https://openalex.org/C523394659","wikidata":"https://www.wikidata.org/wiki/Q17086892","display_name":"Variational analysis","level":2,"score":0.49106669425964355},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36684244871139526},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25577491521835327},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16815689206123352},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s001860050020","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s001860050020","pdf_url":null,"source":{"id":"https://openalex.org/S126160977","display_name":"Mathematical Methods of Operations Research","issn_l":"1432-2994","issn":["1432-2994","1432-5217"],"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 Methods of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:compst:v:48:y:1998:i:2:p:181-186","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s001860050020","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":"","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1484024929","https://openalex.org/W2018127805","https://openalex.org/W2084726813"],"related_works":["https://openalex.org/W2101492045","https://openalex.org/W2060398770","https://openalex.org/W2374035537","https://openalex.org/W330957227","https://openalex.org/W2133881662","https://openalex.org/W1634819625","https://openalex.org/W1974908020","https://openalex.org/W2342725190","https://openalex.org/W1986618495","https://openalex.org/W1970476676"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
