{"id":"https://openalex.org/W2011995039","doi":"https://doi.org/10.1007/s11590-012-0463-y","title":"Normal subdifferentials of efficient point multifunctions in parametric vector optimization","display_name":"Normal subdifferentials of efficient point multifunctions in parametric vector optimization","publication_year":2012,"publication_date":"2012-03-12","ids":{"openalex":"https://openalex.org/W2011995039","doi":"https://doi.org/10.1007/s11590-012-0463-y","mag":"2011995039"},"language":"en","primary_location":{"id":"doi:10.1007/s11590-012-0463-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-012-0463-y","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":"Optimization Letters","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/A5024668916","display_name":"Th\u00e1i Do\u00e3n Ch\u01b0\u01a1ng","orcid":"https://orcid.org/0000-0003-0893-5604"},"institutions":[{"id":"https://openalex.org/I47807185","display_name":"Saigon University","ror":"https://ror.org/01f1fsr30","country_code":"VN","type":"education","lineage":["https://openalex.org/I47807185"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Thai Doan Chuong","raw_affiliation_strings":["Department of Mathematics and Applications, Saigon University, 273 An Duong Vuong Street, Ward 3, District 5, Ho Chi Minh, Vietnam","Saigon University"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Applications, Saigon University, 273 An Duong Vuong Street, Ward 3, District 5, Ho Chi Minh, Vietnam","institution_ids":["https://openalex.org/I47807185"]},{"raw_affiliation_string":"Saigon University","institution_ids":["https://openalex.org/I47807185"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5024668916"],"corresponding_institution_ids":["https://openalex.org/I47807185"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.6959,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.70820743,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"7","issue":"6","first_page":"1087","last_page":"1117"},"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":0.9988999962806702,"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/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.9657999873161316,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.8254314661026001},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.741425633430481},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.6735197305679321},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.6610144376754761},{"id":"https://openalex.org/keywords/computational-intelligence","display_name":"Computational intelligence","score":0.6043724417686462},{"id":"https://openalex.org/keywords/vector-optimization","display_name":"Vector optimization","score":0.5652610063552856},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.551718533039093},{"id":"https://openalex.org/keywords/parametric-programming","display_name":"Parametric programming","score":0.4943275451660156},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4849953353404999},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4630793035030365},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4345833957195282},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4299566149711609},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4186054766178131},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3501678705215454},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22614344954490662},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13816341757774353},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.12181246280670166},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.08185067772865295},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07066884636878967}],"concepts":[{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.8254314661026001},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.741425633430481},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.6735197305679321},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.6610144376754761},{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.6043724417686462},{"id":"https://openalex.org/C164088818","wikidata":"https://www.wikidata.org/wiki/Q7917833","display_name":"Vector optimization","level":4,"score":0.5652610063552856},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.551718533039093},{"id":"https://openalex.org/C2776045410","wikidata":"https://www.wikidata.org/wiki/Q25111241","display_name":"Parametric programming","level":3,"score":0.4943275451660156},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4849953353404999},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4630793035030365},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4345833957195282},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4299566149711609},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4186054766178131},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3501678705215454},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22614344954490662},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13816341757774353},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.12181246280670166},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.08185067772865295},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07066884636878967},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11590-012-0463-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-012-0463-y","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":"Optimization Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309617","display_name":"National Foundation for Science and Technology Development","ror":"https://ror.org/04rw64z44"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W83112366","https://openalex.org/W139036254","https://openalex.org/W417516028","https://openalex.org/W834472104","https://openalex.org/W1493492050","https://openalex.org/W1494303428","https://openalex.org/W1528330203","https://openalex.org/W1884296468","https://openalex.org/W1981718120","https://openalex.org/W1984907879","https://openalex.org/W1990023680","https://openalex.org/W1991006480","https://openalex.org/W2014211093","https://openalex.org/W2023252401","https://openalex.org/W2031840936","https://openalex.org/W2037767943","https://openalex.org/W2045526123","https://openalex.org/W2055448128","https://openalex.org/W2058658058","https://openalex.org/W2063081872","https://openalex.org/W2063333239","https://openalex.org/W2063828056","https://openalex.org/W2064106379","https://openalex.org/W2092191703","https://openalex.org/W2094131264","https://openalex.org/W2112141058","https://openalex.org/W2136449272","https://openalex.org/W2136553956","https://openalex.org/W2138278189","https://openalex.org/W2153562582","https://openalex.org/W2235484001","https://openalex.org/W2284819150","https://openalex.org/W2869708730","https://openalex.org/W3157341860","https://openalex.org/W3191026888","https://openalex.org/W4212924444","https://openalex.org/W4233295974","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3110411377","https://openalex.org/W4308905590","https://openalex.org/W2013374813","https://openalex.org/W2040739535","https://openalex.org/W2388375429","https://openalex.org/W2381571088","https://openalex.org/W2036474185","https://openalex.org/W1974710989","https://openalex.org/W1992155926","https://openalex.org/W2040682926"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
