{"id":"https://openalex.org/W1981090351","doi":"https://doi.org/10.1007/s10957-012-0076-8","title":"Second-Order Optimality Conditions for Strict Efficiency of Constrained Set-Valued Optimization","display_name":"Second-Order Optimality Conditions for Strict Efficiency of Constrained Set-Valued Optimization","publication_year":2012,"publication_date":"2012-05-11","ids":{"openalex":"https://openalex.org/W1981090351","doi":"https://doi.org/10.1007/s10957-012-0076-8","mag":"1981090351"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-012-0076-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-012-0076-8","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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 Optimization Theory and Applications","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/A5022599849","display_name":"Sichen Li","orcid":"https://orcid.org/0000-0001-6045-4395"},"institutions":[{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"S. J. Li","raw_affiliation_strings":["College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China","Mathematical Sciences Research Institute in Chongqing, Chongqing University, Chongqing, 401331, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China","institution_ids":["https://openalex.org/I158842170"]},{"raw_affiliation_string":"Mathematical Sciences Research Institute in Chongqing, Chongqing University, Chongqing, 401331, China","institution_ids":["https://openalex.org/I158842170"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087791261","display_name":"Shengkun Zhu","orcid":"https://orcid.org/0000-0001-8569-124X"},"institutions":[{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"S. K. Zhu","raw_affiliation_strings":["College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China","institution_ids":["https://openalex.org/I158842170"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027557531","display_name":"Xuan-Kun Li","orcid":"https://orcid.org/0009-0003-9114-0171"},"institutions":[{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"X. B. Li","raw_affiliation_strings":["College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China","institution_ids":["https://openalex.org/I158842170"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5022599849"],"corresponding_institution_ids":["https://openalex.org/I158842170"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.7397,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.83901219,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"155","issue":"2","first_page":"534","last_page":"557"},"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":0.9934999942779541,"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":0.9546999931335449,"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":0.778952956199646},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.7581496834754944},{"id":"https://openalex.org/keywords/vector-optimization","display_name":"Vector optimization","score":0.6892500519752502},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6334693431854248},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6016289591789246},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5484127402305603},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5221959948539734},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.49758341908454895},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17556002736091614},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1532829999923706}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.778952956199646},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.7581496834754944},{"id":"https://openalex.org/C164088818","wikidata":"https://www.wikidata.org/wiki/Q7917833","display_name":"Vector optimization","level":4,"score":0.6892500519752502},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6334693431854248},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6016289591789246},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5484127402305603},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5221959948539734},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.49758341908454895},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17556002736091614},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1532829999923706},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-012-0076-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-012-0076-8","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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 Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:joptap:v:155:y:2012:i:2:d:10.1007_s10957-012-0076-8","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-012-0076-8","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":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.6100000143051147}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W139036254","https://openalex.org/W1484024929","https://openalex.org/W1495508859","https://openalex.org/W1585268704","https://openalex.org/W1601741115","https://openalex.org/W1972675155","https://openalex.org/W1975708545","https://openalex.org/W1994120194","https://openalex.org/W2013118573","https://openalex.org/W2014872322","https://openalex.org/W2017898167","https://openalex.org/W2017942050","https://openalex.org/W2022828798","https://openalex.org/W2027200819","https://openalex.org/W2027449074","https://openalex.org/W2041037772","https://openalex.org/W2053930141","https://openalex.org/W2069506584","https://openalex.org/W2069876296","https://openalex.org/W2069936656","https://openalex.org/W2070088208","https://openalex.org/W2083987548","https://openalex.org/W2085163586","https://openalex.org/W2100384283","https://openalex.org/W2117463942","https://openalex.org/W2139548281","https://openalex.org/W2149187637","https://openalex.org/W2166701438","https://openalex.org/W2595644070","https://openalex.org/W4249513058","https://openalex.org/W4252722163"],"related_works":["https://openalex.org/W2138511311","https://openalex.org/W2028885955","https://openalex.org/W2565276936","https://openalex.org/W2766340440","https://openalex.org/W4385713703","https://openalex.org/W1733367267","https://openalex.org/W2072886676","https://openalex.org/W1989726050","https://openalex.org/W109016340","https://openalex.org/W188711498"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
