{"id":"https://openalex.org/W2008221649","doi":"https://doi.org/10.1137/s1052623401384850","title":"Nonlinear Lagrangian for Multiobjective Optimization and Applications to Duality and Exact Penalization","display_name":"Nonlinear Lagrangian for Multiobjective Optimization and Applications to Duality and Exact Penalization","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2008221649","doi":"https://doi.org/10.1137/s1052623401384850","mag":"2008221649"},"language":"en","primary_location":{"id":"doi:10.1137/s1052623401384850","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623401384850","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/5884/1/Huang_Nonlinear_Lagrangian_Duality.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028578315","display_name":"Xiaoxu Huang","orcid":"https://orcid.org/0000-0002-4635-6112"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"X. X. Huang","raw_affiliation_strings":["Department of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, People's Republic of China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024523994","display_name":"Xiaoqi Yang","orcid":"https://orcid.org/0000-0002-5583-4032"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"X. Q. Yang","raw_affiliation_strings":["Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I14243506"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5028578315"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7497,"has_fulltext":true,"cited_by_count":30,"citation_normalized_percentile":{"value":0.83929505,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"13","issue":"3","first_page":"675","last_page":"692"},"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":0.9984999895095825,"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":0.9696999788284302,"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/mathematics","display_name":"Mathematics","score":0.7605782747268677},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.7074782848358154},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.603746771812439},{"id":"https://openalex.org/keywords/infimum-and-supremum","display_name":"Infimum and supremum","score":0.5925295948982239},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.5821333527565002},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.5714685916900635},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5634886622428894},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.5392206311225891},{"id":"https://openalex.org/keywords/wolfe-duality","display_name":"Wolfe duality","score":0.5331774353981018},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.5231534242630005},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5177232623100281},{"id":"https://openalex.org/keywords/duality-gap","display_name":"Duality gap","score":0.48023802042007446},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.45300236344337463},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.4446217715740204},{"id":"https://openalex.org/keywords/weak-duality","display_name":"Weak duality","score":0.44058820605278015},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4304021894931793},{"id":"https://openalex.org/keywords/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.42609187960624695},{"id":"https://openalex.org/keywords/calmness","display_name":"Calmness","score":0.4228157699108124},{"id":"https://openalex.org/keywords/vector-optimization","display_name":"Vector optimization","score":0.4123711585998535},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38746193051338196},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11742249131202698},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.05612248182296753}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7605782747268677},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.7074782848358154},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.603746771812439},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.5925295948982239},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.5821333527565002},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.5714685916900635},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5634886622428894},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.5392206311225891},{"id":"https://openalex.org/C109456813","wikidata":"https://www.wikidata.org/wiki/Q8029991","display_name":"Wolfe duality","level":5,"score":0.5331774353981018},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.5231534242630005},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5177232623100281},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.48023802042007446},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.45300236344337463},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.4446217715740204},{"id":"https://openalex.org/C80682859","wikidata":"https://www.wikidata.org/wiki/Q7977943","display_name":"Weak duality","level":4,"score":0.44058820605278015},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4304021894931793},{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.42609187960624695},{"id":"https://openalex.org/C2778712213","wikidata":"https://www.wikidata.org/wiki/Q20740046","display_name":"Calmness","level":2,"score":0.4228157699108124},{"id":"https://openalex.org/C164088818","wikidata":"https://www.wikidata.org/wiki/Q7917833","display_name":"Vector optimization","level":4,"score":0.4123711585998535},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38746193051338196},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11742249131202698},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.05612248182296753},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C118552586","wikidata":"https://www.wikidata.org/wiki/Q7867","display_name":"Psychiatry","level":1,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s1052623401384850","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623401384850","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/5884","is_oa":true,"landing_page_url":"http://hdl.handle.net/10397/5884","pdf_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/5884/1/Huang_Nonlinear_Lagrangian_Duality.pdf","source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"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":"Journal/Magazine Article"}],"best_oa_location":{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/5884","is_oa":true,"landing_page_url":"http://hdl.handle.net/10397/5884","pdf_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/5884/1/Huang_Nonlinear_Lagrangian_Duality.pdf","source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"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":"Journal/Magazine Article"},"sustainable_development_goals":[{"score":0.6600000262260437,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2008221649.pdf","grobid_xml":"https://content.openalex.org/works/W2008221649.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W56167471","https://openalex.org/W58439901","https://openalex.org/W113278869","https://openalex.org/W1481747975","https://openalex.org/W1507925093","https://openalex.org/W1551360398","https://openalex.org/W1577338488","https://openalex.org/W1968933161","https://openalex.org/W1979028018","https://openalex.org/W1985319797","https://openalex.org/W1995340188","https://openalex.org/W1997231674","https://openalex.org/W1997586153","https://openalex.org/W2013375817","https://openalex.org/W2036833017","https://openalex.org/W2041640046","https://openalex.org/W2042153418","https://openalex.org/W2063529817","https://openalex.org/W2078762555","https://openalex.org/W2090888795","https://openalex.org/W2787523326","https://openalex.org/W2802620382","https://openalex.org/W4240561492","https://openalex.org/W4242576043","https://openalex.org/W4249125060","https://openalex.org/W4249513058","https://openalex.org/W4293820388"],"related_works":["https://openalex.org/W4220928172","https://openalex.org/W2029896594","https://openalex.org/W3213165575","https://openalex.org/W640885572","https://openalex.org/W2345066843","https://openalex.org/W2056178476","https://openalex.org/W2384039353","https://openalex.org/W2241982889","https://openalex.org/W4224273196","https://openalex.org/W578535666"],"abstract_inverted_index":{"Duality":[0],"and":[1,12,31,34,40,53,76],"penalty":[2,13,32,42],"methods":[3,14],"are":[4],"popular":[5],"in":[6],"optimization.":[7],"The":[8,57],"study":[9],"on":[10],"duality":[11,52,59],"for":[15,44],"nonconvex":[16],"multiobjective":[17,45,72],"optimization":[18,47,74],"problems":[19,39,43],"is":[20,60,86],"very":[21],"limited.":[22],"In":[23],"this":[24],"paper,":[25],"we":[26],"introduce":[27],"vector-valued":[28],"nonlinear":[29,36,41,80],"Lagrangian":[30,37,81],"functions":[33],"formulate":[35],"dual":[38,82],"constrained":[46,73],"problems.":[48],"We":[49],"establish":[50],"strong":[51,58],"exact":[54],"penalization":[55,85],"results.":[56],"an":[61],"inclusion":[62],"between":[63],"the":[64,70,79],"set":[65],"of":[66,69,78],"infimum":[67],"points":[68],"original":[71],"problem":[75],"that":[77],"problem.":[83],"Exact":[84],"established":[87],"via":[88],"a":[89],"generalized":[90],"calmness-type":[91],"condition.":[92]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
