{"id":"https://openalex.org/W3044125076","doi":"https://doi.org/10.1007/s10898-020-00935-7","title":"Second-order KKT optimality conditions for multiobjective discrete optimal control problems","display_name":"Second-order KKT optimality conditions for multiobjective discrete optimal control problems","publication_year":2020,"publication_date":"2020-07-24","ids":{"openalex":"https://openalex.org/W3044125076","doi":"https://doi.org/10.1007/s10898-020-00935-7","mag":"3044125076"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-020-00935-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-020-00935-7","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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 Global Optimization","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/A5084175450","display_name":"N. T. Toan","orcid":null},"institutions":[{"id":"https://openalex.org/I94518387","display_name":"Hanoi University of Science and Technology","ror":"https://ror.org/04nyv3z04","country_code":"VN","type":"education","lineage":["https://openalex.org/I94518387"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Nguyen Thi Toan","raw_affiliation_strings":["School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam","institution_ids":["https://openalex.org/I94518387"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078527522","display_name":"L. Q. Thuy","orcid":null},"institutions":[{"id":"https://openalex.org/I94518387","display_name":"Hanoi University of Science and Technology","ror":"https://ror.org/04nyv3z04","country_code":"VN","type":"education","lineage":["https://openalex.org/I94518387"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Le Quang Thuy","raw_affiliation_strings":["School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam","institution_ids":["https://openalex.org/I94518387"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061100646","display_name":"Nguy\u1ec5n V\u0103n Tuy\u00ean","orcid":"https://orcid.org/0000-0003-1920-310X"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]},{"id":"https://openalex.org/I4210095523","display_name":"Hanoi Pedagogical University 2","ror":"https://ror.org/00st18g74","country_code":"VN","type":"education","lineage":["https://openalex.org/I4210095523"]}],"countries":["CN","VN"],"is_corresponding":false,"raw_author_name":"Nguyen Van Tuyen","raw_affiliation_strings":["Department of Mathematics, Hanoi Pedagogical University 2, Xuan Hoa, Phuc Yen, Vinh Phuc, Vietnam","School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, People\u2019s Republic of China","School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hanoi Pedagogical University 2, Xuan Hoa, Phuc Yen, Vinh Phuc, Vietnam","institution_ids":["https://openalex.org/I4210095523"]},{"raw_affiliation_string":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, People\u2019s Republic of China","institution_ids":["https://openalex.org/I150229711"]},{"raw_affiliation_string":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, People's Republic of China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080881249","display_name":"Yi\u2010bin Xiao","orcid":"https://orcid.org/0000-0002-0676-7662"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yi-Bin Xiao","raw_affiliation_strings":["School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, People\u2019s Republic of China","School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, People\u2019s Republic of China","institution_ids":["https://openalex.org/I150229711"]},{"raw_affiliation_string":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, People's Republic of China","institution_ids":["https://openalex.org/I150229711"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5084175450"],"corresponding_institution_ids":["https://openalex.org/I94518387"],"apc_list":{"value":2780,"currency":"USD","value_usd":2780},"apc_paid":null,"fwci":0.8865,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.79865827,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"79","issue":"1","first_page":"203","last_page":"231"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9987999796867371,"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":0.9987999796867371,"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/T13855","display_name":"Aerospace Engineering and Control Systems","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.982200026512146,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/karush\u2013kuhn\u2013tucker-conditions","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","score":0.9339364767074585},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8491171598434448},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6974402666091919},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6887041926383972},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5265724658966064},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5096495151519775},{"id":"https://openalex.org/keywords/optimality-criterion","display_name":"Optimality criterion","score":0.5007383823394775},{"id":"https://openalex.org/keywords/pareto-optimal","display_name":"Pareto optimal","score":0.450632780790329},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4195687770843506},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.41500580310821533},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.414841890335083},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.3482207655906677},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11025258898735046},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.054710447788238525}],"concepts":[{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.9339364767074585},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8491171598434448},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6974402666091919},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6887041926383972},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5265724658966064},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5096495151519775},{"id":"https://openalex.org/C2778153524","wikidata":"https://www.wikidata.org/wiki/Q4241335","display_name":"Optimality criterion","level":2,"score":0.5007383823394775},{"id":"https://openalex.org/C2986314615","wikidata":"https://www.wikidata.org/wiki/Q36829","display_name":"Pareto optimal","level":3,"score":0.450632780790329},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4195687770843506},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.41500580310821533},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.414841890335083},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.3482207655906677},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11025258898735046},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.054710447788238525},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10898-020-00935-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-020-00935-7","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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 Global Optimization","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:jglopt:v:79:y:2021:i:1:d:10.1007_s10898-020-00935-7","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10898-020-00935-7","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W564300562","https://openalex.org/W1659904137","https://openalex.org/W1965288599","https://openalex.org/W1965381995","https://openalex.org/W1983871704","https://openalex.org/W1985296887","https://openalex.org/W1992769584","https://openalex.org/W1995576098","https://openalex.org/W1998235498","https://openalex.org/W2002371412","https://openalex.org/W2005309083","https://openalex.org/W2017898167","https://openalex.org/W2028325686","https://openalex.org/W2035876718","https://openalex.org/W2036602540","https://openalex.org/W2037738670","https://openalex.org/W2042810077","https://openalex.org/W2046992150","https://openalex.org/W2048025921","https://openalex.org/W2056543988","https://openalex.org/W2070066709","https://openalex.org/W2071324182","https://openalex.org/W2074190491","https://openalex.org/W2090882161","https://openalex.org/W2091703679","https://openalex.org/W2144865371","https://openalex.org/W2147826718","https://openalex.org/W2153562582","https://openalex.org/W2157005917","https://openalex.org/W2158468799","https://openalex.org/W2221178412","https://openalex.org/W2523511221","https://openalex.org/W2557774346","https://openalex.org/W2557779326","https://openalex.org/W2596396145","https://openalex.org/W2803389929","https://openalex.org/W2811385795","https://openalex.org/W2964300933","https://openalex.org/W3029645440","https://openalex.org/W3035658569","https://openalex.org/W3125760711","https://openalex.org/W3125882718","https://openalex.org/W3157341860","https://openalex.org/W4249513058","https://openalex.org/W4252738251","https://openalex.org/W4285719527","https://openalex.org/W4293775970"],"related_works":["https://openalex.org/W2090401866","https://openalex.org/W2337862504","https://openalex.org/W2123512339","https://openalex.org/W1979141062","https://openalex.org/W159345135","https://openalex.org/W4289753243","https://openalex.org/W2084351816","https://openalex.org/W2310143336","https://openalex.org/W4235804352","https://openalex.org/W3044125076"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}