{"id":"https://openalex.org/W2921071990","doi":"https://doi.org/10.3233/jcm-190014","title":"Canonical dual methods for general box constrained nonconvex and nonsmooth optimization problems","display_name":"Canonical dual methods for general box constrained nonconvex and nonsmooth optimization problems","publication_year":2019,"publication_date":"2019-03-08","ids":{"openalex":"https://openalex.org/W2921071990","doi":"https://doi.org/10.3233/jcm-190014","mag":"2921071990"},"language":"en","primary_location":{"id":"doi:10.3233/jcm-190014","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jcm-190014","pdf_url":null,"source":{"id":"https://openalex.org/S2765058733","display_name":"Journal of Computational Methods in Sciences and Engineering","issn_l":"1472-7978","issn":["1472-7978","1875-8983"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Methods in Sciences and Engineering","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/A5007949543","display_name":"Huicheng C. Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I153473198","display_name":"North China Electric Power University","ror":"https://ror.org/04qr5t414","country_code":"CN","type":"education","lineage":["https://openalex.org/I153473198"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Huicheng C. Liu","raw_affiliation_strings":["Beijing Key Laboratory of New Energy and Low-Carbon Development, North China Electric Power University, Beijing, China","School of Economics and Management, North China Electric Power University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Beijing Key Laboratory of New Energy and Low-Carbon Development, North China Electric Power University, Beijing, China","institution_ids":["https://openalex.org/I153473198"]},{"raw_affiliation_string":"School of Economics and Management, North China Electric Power University, Beijing, China","institution_ids":["https://openalex.org/I153473198"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101953283","display_name":"Jianwei Gao","orcid":"https://orcid.org/0000-0003-4203-0374"},"institutions":[{"id":"https://openalex.org/I153473198","display_name":"North China Electric Power University","ror":"https://ror.org/04qr5t414","country_code":"CN","type":"education","lineage":["https://openalex.org/I153473198"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianwei Gao","raw_affiliation_strings":["Beijing Key Laboratory of New Energy and Low-Carbon Development, North China Electric Power University, Beijing, China","School of Economics and Management, North China Electric Power University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Beijing Key Laboratory of New Energy and Low-Carbon Development, North China Electric Power University, Beijing, China","institution_ids":["https://openalex.org/I153473198"]},{"raw_affiliation_string":"School of Economics and Management, North China Electric Power University, Beijing, China","institution_ids":["https://openalex.org/I153473198"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100375038","display_name":"Jing Liu","orcid":"https://orcid.org/0000-0002-6834-5350"},"institutions":[{"id":"https://openalex.org/I4210151615","display_name":"Wuyi University","ror":"https://ror.org/0488wz367","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210151615"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jing Liu","raw_affiliation_strings":["Department of Mathematics and Computing Science, Wuyi University, Guangdong, Jiangmen, China","E-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computing Science, Wuyi University, Guangdong, Jiangmen, China","institution_ids":["https://openalex.org/I4210151615"]},{"raw_affiliation_string":"E-mail:","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5007949543"],"corresponding_institution_ids":["https://openalex.org/I153473198"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04615017,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"3","first_page":"765","last_page":"777"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9993000030517578,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9991999864578247,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/triality","display_name":"Triality","score":0.9591513276100159},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.7464630603790283},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.6702102422714233},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.5934190154075623},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5647791028022766},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5171558260917664},{"id":"https://openalex.org/keywords/canonical-transformation","display_name":"Canonical transformation","score":0.5064667463302612},{"id":"https://openalex.org/keywords/duality-gap","display_name":"Duality gap","score":0.5032395720481873},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.488591730594635},{"id":"https://openalex.org/keywords/constrained-optimization-problem","display_name":"Constrained optimization problem","score":0.43138957023620605},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.42509007453918457},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15292006731033325},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07511436939239502}],"concepts":[{"id":"https://openalex.org/C83716740","wikidata":"https://www.wikidata.org/wiki/Q17104294","display_name":"Triality","level":2,"score":0.9591513276100159},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.7464630603790283},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.6702102422714233},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5934190154075623},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5647791028022766},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5171558260917664},{"id":"https://openalex.org/C161520196","wikidata":"https://www.wikidata.org/wiki/Q1366892","display_name":"Canonical transformation","level":3,"score":0.5064667463302612},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.5032395720481873},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.488591730594635},{"id":"https://openalex.org/C2989514635","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization problem","level":3,"score":0.43138957023620605},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.42509007453918457},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15292006731033325},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07511436939239502},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/jcm-190014","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jcm-190014","pdf_url":null,"source":{"id":"https://openalex.org/S2765058733","display_name":"Journal of Computational Methods in Sciences and Engineering","issn_l":"1472-7978","issn":["1472-7978","1875-8983"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Methods in Sciences and Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W8102976","https://openalex.org/W52048609","https://openalex.org/W587390710","https://openalex.org/W1529767900","https://openalex.org/W1570966183","https://openalex.org/W1964780654","https://openalex.org/W1968142821","https://openalex.org/W1972604104","https://openalex.org/W1994794468","https://openalex.org/W2051318200","https://openalex.org/W2053770324","https://openalex.org/W2064646007","https://openalex.org/W2519665767","https://openalex.org/W2898420283","https://openalex.org/W6634144411"],"related_works":["https://openalex.org/W2593555778","https://openalex.org/W2321261235","https://openalex.org/W2201555914","https://openalex.org/W2725387418","https://openalex.org/W2614523486","https://openalex.org/W640885572","https://openalex.org/W4220928172","https://openalex.org/W2089739134","https://openalex.org/W587390710","https://openalex.org/W2921071990"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,24,29],"canonical":[4,25],"duality":[5,68],"theory":[6,17],"for":[7,65],"general":[8,37],"box":[9,38],"constrained":[10,39],"nonconvex":[11,40],"and":[12,28,41,75,80],"nonsmooth":[13],"optimization":[14,44],"problems.":[15],"The":[16,59],"is":[18,33,63],"illustrated":[19],"perfectly":[20],"by":[21],"showing":[22],"mainly":[23],"dual":[26,52,61],"transformation":[27,62],"triality":[30,71],"theory.":[31],"It":[32],"proved":[34],"that":[35],"the":[36,50,67,70],"nonsmoot":[42],"h":[43],"problems":[45],"can":[46,55],"be":[47,56],"changed":[48],"into":[49],"perfect":[51,60],"problems,":[53],"which":[54],"solved":[57],"easily.":[58],"developed":[64],"eliminating":[66],"gap,while":[69],"theorem":[72],"studies":[73],"global":[74],"local":[76],"extreme":[77],"conditions.":[78],"Applications":[79],"examples":[81],"are":[82],"illustrated.":[83]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}