{"id":"https://openalex.org/W200069104","doi":"https://doi.org/10.1007/978-3-642-54265-7_10","title":"Ekeland Variational Principle","display_name":"Ekeland Variational Principle","publication_year":2014,"publication_date":"2014-07-31","ids":{"openalex":"https://openalex.org/W200069104","doi":"https://doi.org/10.1007/978-3-642-54265-7_10","mag":"200069104"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-54265-7_10","doi":"https://doi.org/10.1007/978-3-642-54265-7_10","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-54265-7_10","pdf_url":null,"source":{"id":"https://openalex.org/S4210189481","display_name":"Vector optimization","issn_l":"1867-8971","issn":["1867-8971","1867-898X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Vector Optimization","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W2478963760","display_name":"Set-valued Optimization"},"type":"book-chapter","is_traditional":true,"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/A5013676704","display_name":"Akhtar A. Khan","orcid":"https://orcid.org/0000-0002-8229-6604","observed_orcids":["https://orcid.org/0000-0002-8229-6604"]},"institutions":[{"id":"https://openalex.org/I155173764","display_name":"Rochester Institute of Technology","ror":"https://ror.org/00v4yb702","country_code":"US","type":"education","lineage":["https://openalex.org/I155173764"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Akhtar A. Khan","raw_affiliation_strings":["Rochester Institute of Technology School of Mathematical Sciences, Rochester, New York, USA","Rochester Institute of Technology, School of Mathematical Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rochester Institute of Technology School of Mathematical Sciences, Rochester, New York, USA","institution_ids":["https://openalex.org/I155173764"]},{"raw_affiliation_string":"Rochester Institute of Technology, School of Mathematical Sciences","institution_ids":["https://openalex.org/I155173764"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004850710","display_name":"Christiane Tammer","orcid":"https://orcid.org/0000-0002-4446-9789","observed_orcids":["https://orcid.org/0000-0002-4446-9789"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christiane Tammer","raw_affiliation_strings":["Halle, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Halle, Germany","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034884075","display_name":"Constantin Z\u0103linescu","orcid":"https://orcid.org/0000-0001-8461-818X","observed_orcids":["https://orcid.org/0000-0001-8461-818X"]},"institutions":[{"id":"https://openalex.org/I138164181","display_name":"Alexandru Ioan Cuza University","ror":"https://ror.org/022kvet57","country_code":"RO","type":"education","lineage":["https://openalex.org/I138164181"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Constantin Z\u0103linescu","raw_affiliation_strings":["Faculty of Mathematics, University \u201cAl. I. Cuza\u201d Iasi, Iasi, Romania","University \u201cAl. I. Cuza\u201d Iasi"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University \u201cAl. I. Cuza\u201d Iasi, Iasi, Romania","institution_ids":["https://openalex.org/I138164181"]},{"raw_affiliation_string":"University \u201cAl. I. Cuza\u201d Iasi","institution_ids":["https://openalex.org/I138164181"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.09857724,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"369","last_page":"397"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9682999849319458,"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":0.9682999849319458,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.029899999499320984,"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"}},{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/ekeland-s-variational-principle","display_name":"Ekeland's variational principle","score":0.9869999885559082},{"id":"https://openalex.org/keywords/minimal-points","display_name":"minimal points","score":0.6570000052452087},{"id":"https://openalex.org/keywords/complete-metric-spaces","display_name":"complete metric spaces","score":0.734000027179718},{"id":"https://openalex.org/keywords/topological-vector-spaces","display_name":"topological vector spaces","score":0.9909999966621399},{"id":"https://openalex.org/keywords/order-relations","display_name":"order relations","score":0.7929999828338623},{"id":"https://openalex.org/keywords/scalar-optimization","display_name":"scalar optimization","score":0.6579999923706055},{"id":"https://openalex.org/keywords/error-bounds","display_name":"error bounds","score":0.9850000143051147},{"id":"https://openalex.org/keywords/set-valued-optimization","display_name":"set-valued optimization","score":0.9959999918937683}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7283312678337097},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.7102149128913879},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5638836622238159},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.521234393119812},{"id":"https://openalex.org/C164088818","wikidata":"https://www.wikidata.org/wiki/Q7917833","display_name":"Vector optimization","level":4,"score":0.5035580992698669},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4592463970184326},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44069916009902954},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4381324350833893},{"id":"https://openalex.org/C123222754","wikidata":"https://www.wikidata.org/wiki/Q1070472","display_name":"Product topology","level":2,"score":0.433398962020874},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4328903555870056},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3520888686180115},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34996500611305237},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3229445517063141},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2671114206314087},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2228376865386963},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1639852225780487},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1456613838672638},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07759711146354675},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"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},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-54265-7_10","doi":"https://doi.org/10.1007/978-3-642-54265-7_10","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-54265-7_10","pdf_url":null,"source":{"id":"https://openalex.org/S4210189481","display_name":"Vector optimization","issn_l":"1867-8971","issn":["1867-8971","1867-898X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Vector Optimization","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W17601992","https://openalex.org/W121515171","https://openalex.org/W1582299569","https://openalex.org/W1964620490","https://openalex.org/W1977750299","https://openalex.org/W1980325299","https://openalex.org/W1997201451","https://openalex.org/W1998381876","https://openalex.org/W2003663149","https://openalex.org/W2013118573","https://openalex.org/W2015209305","https://openalex.org/W2024028885","https://openalex.org/W2028552391","https://openalex.org/W2036581185","https://openalex.org/W2047346277","https://openalex.org/W2063333239","https://openalex.org/W2065840522","https://openalex.org/W2084544025","https://openalex.org/W2114605231","https://openalex.org/W2138278189","https://openalex.org/W2163613677","https://openalex.org/W2594483763","https://openalex.org/W4252745766"],"related_works":["https://openalex.org/W4252745766","https://openalex.org/W2165415076","https://openalex.org/W1993071711","https://openalex.org/W2133881662","https://openalex.org/W1986618495","https://openalex.org/W117217602","https://openalex.org/W2088383560","https://openalex.org/W3186432288","https://openalex.org/W2747430392","https://openalex.org/W121515171"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":3}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}