{"id":"https://openalex.org/W2512499967","doi":"https://doi.org/10.1007/s10957-016-0995-x","title":"Second-Order Conditions for Open-Cone Minimizers and Firm Minimizers in Set-Valued Optimization Subject to Mixed Constraints","display_name":"Second-Order Conditions for Open-Cone Minimizers and Firm Minimizers in Set-Valued Optimization Subject to Mixed Constraints","publication_year":2016,"publication_date":"2016-08-22","ids":{"openalex":"https://openalex.org/W2512499967","doi":"https://doi.org/10.1007/s10957-016-0995-x","mag":"2512499967"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-016-0995-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-016-0995-x","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/A5059731357","display_name":"Phan Qu\u1ed1c Kh\u00e1nh","orcid":"https://orcid.org/0000-0002-0524-0498"},"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":"Phan Quoc Khanh","raw_affiliation_strings":["Department of Mathematics, International University, Vietnam National University Hochiminh City, Linh Trung, Thu Duc, Hochiminh City, Vietnam"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, International University, Vietnam National University Hochiminh City, Linh Trung, Thu Duc, Hochiminh City, Vietnam","institution_ids":["https://openalex.org/I123565023"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112751835","display_name":"Nguy\u1ec5n Minh T\u00f9ng","orcid":null},"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":false,"raw_author_name":"Nguyen Minh Tung","raw_affiliation_strings":["Department of Mathematics and Computing, University of Science, Vietnam National University Hochiminh City, Hochiminh City, Vietnam"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computing, University of Science, Vietnam National University Hochiminh City, Hochiminh City, Vietnam","institution_ids":["https://openalex.org/I123565023"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5059731357"],"corresponding_institution_ids":["https://openalex.org/I123565023"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.1557,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.88674706,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"171","issue":"1","first_page":"45","last_page":"69"},"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":0.9980000257492065,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.992900013923645,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.8093204498291016},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7670559883117676},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.7629806995391846},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6422024369239807},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5926553010940552},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5691378712654114},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.47175198793411255},{"id":"https://openalex.org/keywords/karush\u2013kuhn\u2013tucker-conditions","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","score":0.45595529675483704},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.4444929361343384},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4155150353908539},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3550873398780823},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19262772798538208},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.12340766191482544},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06992647051811218}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.8093204498291016},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7670559883117676},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.7629806995391846},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6422024369239807},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5926553010940552},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5691378712654114},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47175198793411255},{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.45595529675483704},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.4444929361343384},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4155150353908539},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3550873398780823},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19262772798538208},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12340766191482544},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06992647051811218},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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/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/s10957-016-0995-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-016-0995-x","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:171:y:2016:i:1:d:10.1007_s10957-016-0995-x","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-016-0995-x","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W135911866","https://openalex.org/W205925530","https://openalex.org/W632378324","https://openalex.org/W1552227532","https://openalex.org/W1609728248","https://openalex.org/W1967619906","https://openalex.org/W1975708545","https://openalex.org/W1979937452","https://openalex.org/W1981090351","https://openalex.org/W1981928753","https://openalex.org/W1983871704","https://openalex.org/W1994120194","https://openalex.org/W2003713910","https://openalex.org/W2014872322","https://openalex.org/W2015832797","https://openalex.org/W2017898167","https://openalex.org/W2018508199","https://openalex.org/W2022828798","https://openalex.org/W2024279814","https://openalex.org/W2027200819","https://openalex.org/W2027449074","https://openalex.org/W2033361820","https://openalex.org/W2039944282","https://openalex.org/W2040953139","https://openalex.org/W2041037772","https://openalex.org/W2063173399","https://openalex.org/W2070088208","https://openalex.org/W2075968870","https://openalex.org/W2085654956","https://openalex.org/W2087164501","https://openalex.org/W2092749636","https://openalex.org/W2114605231","https://openalex.org/W2116598569","https://openalex.org/W2496276084","https://openalex.org/W3105800240","https://openalex.org/W3157341860","https://openalex.org/W4212993107","https://openalex.org/W4231183558","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2155858901","https://openalex.org/W4382519099","https://openalex.org/W2491194410","https://openalex.org/W1515727993","https://openalex.org/W1993702234","https://openalex.org/W4311904729","https://openalex.org/W2137600664","https://openalex.org/W2044122222","https://openalex.org/W2028885955","https://openalex.org/W1733367267"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}