{"id":"https://openalex.org/W2057140727","doi":"https://doi.org/10.1155/2013/383692","title":"Univex Interval-Valued Mapping with Differentiability and Its Application in Nonlinear Programming","display_name":"Univex Interval-Valued Mapping with Differentiability and Its Application in Nonlinear Programming","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2057140727","doi":"https://doi.org/10.1155/2013/383692","mag":"2057140727"},"language":"en","primary_location":{"id":"doi:10.1155/2013/383692","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/383692","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/383692.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2013/383692.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100637033","display_name":"Lifeng Li","orcid":"https://orcid.org/0000-0002-6711-1966"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]},{"id":"https://openalex.org/I4210136859","display_name":"Xi\u2019an University of Posts and Telecommunications","ror":"https://ror.org/04jn0td46","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210136859"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lifeng Li","raw_affiliation_strings":["Department of Mathematics, School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China","Department of Mathematics, School of Science, Xidian University, Xi'an 710126, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China","institution_ids":["https://openalex.org/I4210136859"]},{"raw_affiliation_string":"Department of Mathematics, School of Science, Xidian University, Xi'an 710126, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045137489","display_name":"Sanyang Liu","orcid":"https://orcid.org/0000-0002-3625-3398"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Sanyang Liu","raw_affiliation_strings":["Department of Mathematics, School of Science, Xidian University, Xi'an 710126, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Science, Xidian University, Xi'an 710126, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026174803","display_name":"Jianke Zhang","orcid":"https://orcid.org/0000-0003-0424-5067"},"institutions":[{"id":"https://openalex.org/I4210136859","display_name":"Xi\u2019an University of Posts and Telecommunications","ror":"https://ror.org/04jn0td46","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210136859"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianke Zhang","raw_affiliation_strings":["Department of Mathematics, School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China","institution_ids":["https://openalex.org/I4210136859"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5045137489"],"corresponding_institution_ids":["https://openalex.org/I149594827"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":1.1096,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.79265399,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"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":0.9998000264167786,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.998199999332428,"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/differentiable-function","display_name":"Differentiable function","score":0.8305288553237915},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7669540643692017},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.713623046875},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.6098709106445312},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.5661752223968506},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5608282089233398},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4508424401283264},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4468367099761963},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4271591603755951},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4107668995857239},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29330068826675415},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.19723692536354065},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1431272029876709}],"concepts":[{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.8305288553237915},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7669540643692017},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.713623046875},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.6098709106445312},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.5661752223968506},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5608282089233398},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4508424401283264},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4468367099761963},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4271591603755951},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4107668995857239},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29330068826675415},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.19723692536354065},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1431272029876709},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2013/383692","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/383692","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/383692.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1399493696","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1399493696","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:383692","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2013/383692.xml","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"},{"id":"pmh:oai:doaj.org/article:3ff1d529abbc47f2879d12189814899b","is_oa":true,"landing_page_url":"https://doaj.org/article/3ff1d529abbc47f2879d12189814899b","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/383692","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/383692","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/383692.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1867487515","display_name":null,"funder_award_id":"2013JK1098","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2310858199","display_name":null,"funder_award_id":"2013JK1182","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5684367226","display_name":null,"funder_award_id":"11JK1051","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7410037662","display_name":null,"funder_award_id":"2013JK1130","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G916648127","display_name":null,"funder_award_id":"60974082","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320325627","display_name":"Education Department of Shaanxi Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2057140727.pdf","grobid_xml":"https://content.openalex.org/works/W2057140727.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W42041721","https://openalex.org/W152862786","https://openalex.org/W196661096","https://openalex.org/W1483874187","https://openalex.org/W1559320069","https://openalex.org/W1983098215","https://openalex.org/W1984358873","https://openalex.org/W2000983337","https://openalex.org/W2001359285","https://openalex.org/W2003644018","https://openalex.org/W2006159242","https://openalex.org/W2030129759","https://openalex.org/W2034038007","https://openalex.org/W2041643631","https://openalex.org/W2046715566","https://openalex.org/W2079508853","https://openalex.org/W2083592805","https://openalex.org/W2088735768","https://openalex.org/W2094514915","https://openalex.org/W2146795783"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W4327738859","https://openalex.org/W2348722996","https://openalex.org/W2334570605","https://openalex.org/W3181683615","https://openalex.org/W4286826125","https://openalex.org/W1633485514","https://openalex.org/W2126146763","https://openalex.org/W2026801600","https://openalex.org/W4289943123"],"abstract_inverted_index":{"Interval-valued":[0],"univex":[1,25],"functions":[2],"are":[3,13],"introduced":[4],"for":[5,15],"differentiable":[6],"programming":[7],"problems.":[8],"Optimality":[9],"and":[10],"duality":[11],"results":[12],"derived":[14],"a":[16],"class":[17],"of":[18],"generalized":[19],"convex":[20],"optimization":[21],"problems":[22],"with":[23],"interval-valued":[24],"functions.":[26]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}
