{"id":"https://openalex.org/W4385365527","doi":"https://doi.org/10.1007/s10479-023-05524-x","title":"Nonconvex multi-period mean-variance portfolio optimization","display_name":"Nonconvex multi-period mean-variance portfolio optimization","publication_year":2023,"publication_date":"2023-07-27","ids":{"openalex":"https://openalex.org/W4385365527","doi":"https://doi.org/10.1007/s10479-023-05524-x"},"language":"en","primary_location":{"id":"doi:10.1007/s10479-023-05524-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10479-023-05524-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10479-023-05524-x.pdf","source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10479-023-05524-x.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026185341","display_name":"Zhongming Wu","orcid":"https://orcid.org/0000-0002-9128-5181"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhongming Wu","raw_affiliation_strings":["School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing, 210044, People\u2019s Republic of China","School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing, 210044, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing, 210044, People\u2019s Republic of China","institution_ids":["https://openalex.org/I200845125"]},{"raw_affiliation_string":"School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing, 210044, People's Republic of China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101213880","display_name":"Guoyu Xie","orcid":null},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guoyu Xie","raw_affiliation_strings":["School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing, 210044, People\u2019s Republic of China","School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing, 210044, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing, 210044, People\u2019s Republic of China","institution_ids":["https://openalex.org/I200845125"]},{"raw_affiliation_string":"School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing, 210044, People's Republic of China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109303259","display_name":"Zhili Ge","orcid":null},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhili Ge","raw_affiliation_strings":["School of Mathematics and Information Science, Nanjing Normal University of Special Education, Nanjing, 210038, People\u2019s Republic of China","School of Mathematics and Information Science, Nanjing Normal University of Special Education, Nanjing, 210038, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, Nanjing Normal University of Special Education, Nanjing, 210038, People\u2019s Republic of China","institution_ids":["https://openalex.org/I152031979"]},{"raw_affiliation_string":"School of Mathematics and Information Science, Nanjing Normal University of Special Education, Nanjing, 210038, People's Republic of China","institution_ids":["https://openalex.org/I152031979"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060944643","display_name":"Valentina De Simone","orcid":"https://orcid.org/0000-0002-3357-5252"},"institutions":[{"id":"https://openalex.org/I197809005","display_name":"University of Campania \"Luigi Vanvitelli\"","ror":"https://ror.org/02kqnpp86","country_code":"IT","type":"education","lineage":["https://openalex.org/I197809005"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Valentina De Simone","raw_affiliation_strings":["Department of Mathematics and Physics, University of Campania \u201cLuigi Vanvitelli\u201d, Caserta, 81100, Italy","Department of Mathematics and Physics, University of Campania \"Luigi Vanvitelli\", Caserta, 81100, Italy"],"raw_orcid":"https://orcid.org/0000-0002-3357-5252","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics, University of Campania \u201cLuigi Vanvitelli\u201d, Caserta, 81100, Italy","institution_ids":["https://openalex.org/I197809005"]},{"raw_affiliation_string":"Department of Mathematics and Physics, University of Campania \"Luigi Vanvitelli\", Caserta, 81100, Italy","institution_ids":["https://openalex.org/I197809005"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5060944643"],"corresponding_institution_ids":["https://openalex.org/I197809005"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.5726,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.79982988,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"332","issue":"1-3","first_page":"617","last_page":"644"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9975000023841858,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9957000017166138,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.7255702018737793},{"id":"https://openalex.org/keywords/portfolio","display_name":"Portfolio","score":0.7057658433914185},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6798580288887024},{"id":"https://openalex.org/keywords/portfolio-optimization","display_name":"Portfolio optimization","score":0.5762956142425537},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5689084529876709},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5545138120651245},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.5472837686538696},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.4941258728504181},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.43372848629951477},{"id":"https://openalex.org/keywords/investment-strategy","display_name":"Investment strategy","score":0.41695359349250793},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.369635671377182},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.15843728184700012},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.13774865865707397},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.07943609356880188}],"concepts":[{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.7255702018737793},{"id":"https://openalex.org/C2780821815","wikidata":"https://www.wikidata.org/wiki/Q5340806","display_name":"Portfolio","level":2,"score":0.7057658433914185},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6798580288887024},{"id":"https://openalex.org/C202655437","wikidata":"https://www.wikidata.org/wiki/Q7231728","display_name":"Portfolio optimization","level":3,"score":0.5762956142425537},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5689084529876709},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5545138120651245},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.5472837686538696},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4941258728504181},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.43372848629951477},{"id":"https://openalex.org/C103144560","wikidata":"https://www.wikidata.org/wiki/Q2670999","display_name":"Investment strategy","level":3,"score":0.41695359349250793},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.369635671377182},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.15843728184700012},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13774865865707397},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.07943609356880188},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C183582576","wikidata":"https://www.wikidata.org/wiki/Q184783","display_name":"Market liquidity","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10479-023-05524-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10479-023-05524-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10479-023-05524-x.pdf","source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:annopr:v:332:y:2024:i:1:d:10.1007_s10479-023-05524-x","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10479-023-05524-x","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":{"id":"doi:10.1007/s10479-023-05524-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10479-023-05524-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10479-023-05524-x.pdf","source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.41999998688697815,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G3955196570","display_name":null,"funder_award_id":"2022M711672","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G6888568542","display_name":null,"funder_award_id":"12001286","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8673521038","display_name":null,"funder_award_id":"12001281","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320325777","display_name":"Universit\u00e0 degli Studi della Campania Luigi Vanvitelli","ror":null},{"id":"https://openalex.org/F4320327794","display_name":"Qinglan Project of Jiangsu Province of China","ror":null},{"id":"https://openalex.org/F4320334079","display_name":"Gruppo Nazionale per il Calcolo Scientifico","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4385365527.pdf"},"referenced_works_count":55,"referenced_works":["https://openalex.org/W1719995771","https://openalex.org/W1821374938","https://openalex.org/W1965125844","https://openalex.org/W1967138577","https://openalex.org/W1999830414","https://openalex.org/W2005120624","https://openalex.org/W2022541060","https://openalex.org/W2027982384","https://openalex.org/W2041781650","https://openalex.org/W2045513909","https://openalex.org/W2056201402","https://openalex.org/W2074682976","https://openalex.org/W2127000676","https://openalex.org/W2128196627","https://openalex.org/W2132621139","https://openalex.org/W2135046866","https://openalex.org/W2151237529","https://openalex.org/W2166956514","https://openalex.org/W2237174617","https://openalex.org/W2516602727","https://openalex.org/W2599699595","https://openalex.org/W2761633770","https://openalex.org/W2769032176","https://openalex.org/W2785011264","https://openalex.org/W2790973836","https://openalex.org/W2796071106","https://openalex.org/W2806329290","https://openalex.org/W2808847270","https://openalex.org/W2886664007","https://openalex.org/W2888472564","https://openalex.org/W2900783448","https://openalex.org/W2922398374","https://openalex.org/W2945001541","https://openalex.org/W2954788275","https://openalex.org/W2962853966","https://openalex.org/W2964011556","https://openalex.org/W3011526999","https://openalex.org/W3092351937","https://openalex.org/W3098950028","https://openalex.org/W3103984481","https://openalex.org/W3121053109","https://openalex.org/W3122675629","https://openalex.org/W3123829977","https://openalex.org/W3125319238","https://openalex.org/W3128135549","https://openalex.org/W3206292229","https://openalex.org/W3207481862","https://openalex.org/W3208831396","https://openalex.org/W4205420919","https://openalex.org/W4205423034","https://openalex.org/W4205808776","https://openalex.org/W4225934559","https://openalex.org/W4289028826","https://openalex.org/W4292363360","https://openalex.org/W6807091881"],"related_works":["https://openalex.org/W1986311305","https://openalex.org/W4360613713","https://openalex.org/W3125148470","https://openalex.org/W2768197547","https://openalex.org/W2055959038","https://openalex.org/W2068727170","https://openalex.org/W4206877017","https://openalex.org/W4225528185","https://openalex.org/W4327779378","https://openalex.org/W2795635811"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper,":[3],"we":[4,34,71],"address":[5],"the":[6,29,49,59,64,107,112],"problem":[7],"of":[8,22,48,78,111],"long-term":[9],"investment":[10],"by":[11,58],"exploring":[12],"optimal":[13],"strategies":[14],"for":[15],"allocating":[16],"wealth":[17],"among":[18],"a":[19,36,73,85],"finite":[20],"number":[21],"assets":[23],"over":[24],"multiple":[25],"periods.":[26],"Based":[27],"on":[28,98],"classical":[30],"Markowitz":[31],"mean-variance":[32],"philosophy,":[33],"develop":[35],"new":[37],"portfolio":[38,50],"optimization":[39],"framework":[40],"which":[41],"can":[42,88],"produce":[43],"sparse":[44],"portfolios.":[45],"The":[46],"sparsity":[47],"at":[51],"each":[52],"and":[53,67,80,109,115],"across":[54],"periods":[55],"is":[56],"characterized":[57],"possibly":[60],"nonconvex":[61,66],"penalties.":[62],"For":[63],"constructed":[65],"nonsmooth":[68],"constrained":[69],"model,":[70],"propose":[72],"generalized":[74],"alternating":[75],"direction":[76],"method":[77],"multipliers":[79],"its":[81],"global":[82],"convergence":[83],"to":[84,105],"stationary":[86],"point":[87],"be":[89],"guaranteed":[90],"theoretically.":[91],"Moreover,":[92],"some":[93],"numerical":[94],"experiments":[95],"are":[96],"conducted":[97],"several":[99],"datasets":[100],"generated":[101],"from":[102],"practical":[103],"applications":[104],"illustrate":[106],"effectiveness":[108],"advantage":[110],"proposed":[113],"model":[114],"solving":[116],"method.":[117]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}
