{"id":"https://openalex.org/W3121929370","doi":"https://doi.org/10.1155/2021/6640781","title":"An Infeasible Incremental Bundle Method for Nonsmooth Optimization Problem Based on CVaR Portfolio","display_name":"An Infeasible Incremental Bundle Method for Nonsmooth Optimization Problem Based on CVaR Portfolio","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3121929370","doi":"https://doi.org/10.1155/2021/6640781","mag":"3121929370"},"language":"en","primary_location":{"id":"doi:10.1155/2021/6640781","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/6640781","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/6640781.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"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":"Complexity","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/complexity/2021/6640781.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013049121","display_name":"Jia-Tong Li","orcid":"https://orcid.org/0000-0001-9408-0870"},"institutions":[{"id":"https://openalex.org/I47689461","display_name":"Northeast Forestry University","ror":"https://ror.org/02yxnh564","country_code":"CN","type":"education","lineage":["https://openalex.org/I47689461"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jia-Tong Li","raw_affiliation_strings":["College of Science, Northeast Forestry University, Harbin 150040, China"],"affiliations":[{"raw_affiliation_string":"College of Science, Northeast Forestry University, Harbin 150040, China","institution_ids":["https://openalex.org/I47689461"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044333609","display_name":"Jie Shen","orcid":"https://orcid.org/0000-0001-6157-3388"},"institutions":[{"id":"https://openalex.org/I153374732","display_name":"Liaoning Normal University","ror":"https://ror.org/04c3cgg32","country_code":"CN","type":"education","lineage":["https://openalex.org/I153374732"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jie Shen","raw_affiliation_strings":["School of Mathematics, Liaoning Normal University, Dalian 116029, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Liaoning Normal University, Dalian 116029, China","institution_ids":["https://openalex.org/I153374732"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036742802","display_name":"Na Xu","orcid":"https://orcid.org/0000-0001-8141-5942"},"institutions":[{"id":"https://openalex.org/I153374732","display_name":"Liaoning Normal University","ror":"https://ror.org/04c3cgg32","country_code":"CN","type":"education","lineage":["https://openalex.org/I153374732"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Na Xu","raw_affiliation_strings":["School of Mathematics, Liaoning Normal University, Dalian 116029, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Liaoning Normal University, Dalian 116029, China","institution_ids":["https://openalex.org/I153374732"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044333609"],"corresponding_institution_ids":["https://openalex.org/I153374732"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01630056,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2021","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T11801","display_name":"Reservoir Engineering and Simulation Methods","score":0.9886000156402588,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/T10067","display_name":"Stochastic processes and financial applications","score":0.9825999736785889,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cvar","display_name":"CVAR","score":0.8493438363075256},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7348117828369141},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.5302965641021729},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5026404857635498},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4643248915672302},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.46408388018608093},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.46350568532943726},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.461927592754364},{"id":"https://openalex.org/keywords/portfolio","display_name":"Portfolio","score":0.44293203949928284},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.430502712726593},{"id":"https://openalex.org/keywords/portfolio-optimization","display_name":"Portfolio optimization","score":0.42852461338043213},{"id":"https://openalex.org/keywords/expected-shortfall","display_name":"Expected shortfall","score":0.2760300636291504},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2667861580848694}],"concepts":[{"id":"https://openalex.org/C2779922397","wikidata":"https://www.wikidata.org/wiki/Q5014755","display_name":"CVAR","level":4,"score":0.8493438363075256},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7348117828369141},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5302965641021729},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5026404857635498},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4643248915672302},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.46408388018608093},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.46350568532943726},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.461927592754364},{"id":"https://openalex.org/C2780821815","wikidata":"https://www.wikidata.org/wiki/Q5340806","display_name":"Portfolio","level":2,"score":0.44293203949928284},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.430502712726593},{"id":"https://openalex.org/C202655437","wikidata":"https://www.wikidata.org/wiki/Q7231728","display_name":"Portfolio optimization","level":3,"score":0.42852461338043213},{"id":"https://openalex.org/C5496284","wikidata":"https://www.wikidata.org/wiki/Q5420856","display_name":"Expected shortfall","level":3,"score":0.2760300636291504},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2667861580848694},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2021/6640781","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/6640781","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/6640781.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"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":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:6640781","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/complexity/2021/6640781.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:a4d5686442804c80bbc5e00cd321abc2","is_oa":true,"landing_page_url":"https://doaj.org/article/a4d5686442804c80bbc5e00cd321abc2","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":"Complexity, Vol 2021 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2021/6640781","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/6640781","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/6640781.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"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":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1869654996","display_name":null,"funder_award_id":"11601061","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/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/G3880525217","display_name":null,"funder_award_id":"61877032","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/G4009049029","display_name":null,"funder_award_id":"Startup","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4547793962","display_name":null,"funder_award_id":"20307009","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5169721444","display_name":null,"funder_award_id":"201901","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G542479854","display_name":null,"funder_award_id":"LQ2019019","funder_id":"https://openalex.org/F4320324560","funder_display_name":"Department of Education of Liaoning Province"},{"id":"https://openalex.org/G5797785011","display_name":null,"funder_award_id":"16010","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7836423780","display_name":null,"funder_award_id":"Liaoning","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8851445243","display_name":null,"funder_award_id":"01061","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/F4320324560","display_name":"Department of Education of Liaoning Province","ror":"https://ror.org/0022v2454"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3121929370.pdf","grobid_xml":"https://content.openalex.org/works/W3121929370.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W356322785","https://openalex.org/W1503443042","https://openalex.org/W2005022214","https://openalex.org/W2033957915","https://openalex.org/W2053457645","https://openalex.org/W2076428552","https://openalex.org/W2083432309","https://openalex.org/W2091371007","https://openalex.org/W2116462758","https://openalex.org/W2332354216","https://openalex.org/W2785442089","https://openalex.org/W3087576977","https://openalex.org/W3097189211","https://openalex.org/W4231893760","https://openalex.org/W4251283917","https://openalex.org/W4291439952"],"related_works":["https://openalex.org/W2087892965","https://openalex.org/W2153830644","https://openalex.org/W2078547130","https://openalex.org/W2508928688","https://openalex.org/W1131746181","https://openalex.org/W2750201565","https://openalex.org/W3121390367","https://openalex.org/W2133635752","https://openalex.org/W2017332597","https://openalex.org/W2106063437"],"abstract_inverted_index":{"For":[0],"CVaR":[1],"(conditional":[2],"value\u2010at\u2010risk)":[3],"portfolio":[4],"nonsmooth":[5],"optimization":[6],"problem,":[7],"we":[8,66],"propose":[9],"an":[10],"infeasible":[11],"incremental":[12,27],"bundle":[13,79],"method":[14,28,123],"on":[15],"the":[16,19,23,40,43,55,63,68,82,94,100,106,110,119,125,129,135],"basis":[17],"of":[18,26,42,50,70,84,96,102,109,127],"improvement":[20,59],"function":[21,45,49],"and":[22,46,87,99,105],"main":[24],"idea":[25],"for":[29,58],"solving":[30],"convex":[31],"finite":[32],"min\u2010max":[33],"problems.":[34],"The":[35],"presented":[36],"algorithm":[37,90,111,136],"only":[38],"employs":[39],"information":[41,69],"objective":[44,103],"one":[47],"component":[48],"constraint":[51,131],"functions":[52],"to":[53,80,138],"form":[54],"approximate":[56],"model":[57],"function.":[60],"By":[61],"introducing":[62],"aggregate":[64],"technique,":[65],"keep":[67],"previous":[71],"iterate":[72,97],"points":[73,98],"that":[74],"may":[75],"be":[76],"deleted":[77],"from":[78],"overcome":[81],"difficulty":[83],"numerical":[85],"computation":[86],"storage.":[88],"Our":[89],"does":[91],"not":[92],"enforce":[93],"feasibility":[95],"monotonicity":[101],"function,":[104,132],"global":[107],"convergence":[108],"is":[112],"established":[113],"under":[114],"mild":[115],"conditions.":[116],"Compared":[117],"with":[118],"available":[120],"results,":[121],"our":[122],"loosens":[124],"requirements":[126],"computing":[128],"whole":[130],"which":[133],"makes":[134],"easier":[137],"implement.":[139]},"counts_by_year":[],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}
