{"id":"https://openalex.org/W4385656497","doi":"https://doi.org/10.1109/tpami.2023.3303227","title":"Value-Function-Based Sequential Minimization for Bi-Level Optimization","display_name":"Value-Function-Based Sequential Minimization for Bi-Level Optimization","publication_year":2023,"publication_date":"2023-08-08","ids":{"openalex":"https://openalex.org/W4385656497","doi":"https://doi.org/10.1109/tpami.2023.3303227","pmid":"https://pubmed.ncbi.nlm.nih.gov/37552592"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2023.3303227","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2023.3303227","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5042370642","display_name":"Risheng Liu","orcid":"https://orcid.org/0000-0002-9554-0565"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Risheng Liu","raw_affiliation_strings":["DUT-RU International School of Information Science and Engineering, Dalian University of Technology, Dalian, China","Key Laboratory for Ubiquitous Network and Service Software of Liaoning Province, Dalian, China"],"affiliations":[{"raw_affiliation_string":"DUT-RU International School of Information Science and Engineering, Dalian University of Technology, Dalian, China","institution_ids":["https://openalex.org/I27357992"]},{"raw_affiliation_string":"Key Laboratory for Ubiquitous Network and Service Software of Liaoning Province, Dalian, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101636994","display_name":"Xuan Liu","orcid":"https://orcid.org/0000-0003-4373-1359"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuan Liu","raw_affiliation_strings":["DUT-RU International School of Information Science and Engineering, Dalian University of Technology, Dalian, China","Key Laboratory for Ubiquitous Network and Service Software of Liaoning Province, Dalian, China"],"affiliations":[{"raw_affiliation_string":"DUT-RU International School of Information Science and Engineering, Dalian University of Technology, Dalian, China","institution_ids":["https://openalex.org/I27357992"]},{"raw_affiliation_string":"Key Laboratory for Ubiquitous Network and Service Software of Liaoning Province, Dalian, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014555178","display_name":"Shangzhi Zeng","orcid":"https://orcid.org/0000-0002-6950-7825"},"institutions":[{"id":"https://openalex.org/I212119943","display_name":"University of Victoria","ror":"https://ror.org/04s5mat29","country_code":"CA","type":"education","lineage":["https://openalex.org/I212119943"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Shangzhi Zeng","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada","institution_ids":["https://openalex.org/I212119943"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080552363","display_name":"Jin Zhang","orcid":"https://orcid.org/0000-0002-6691-5612"},"institutions":[{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]},{"id":"https://openalex.org/I4210136793","display_name":"Peng Cheng Laboratory","ror":"https://ror.org/03qdqbt06","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210136793"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jin Zhang","raw_affiliation_strings":["Department of Mathematics, SUSTech International Center for Mathematics, Southern University of Science and Technology, National Center for Applied Mathematics Shenzhen, and Peng Cheng Laboratory, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, SUSTech International Center for Mathematics, Southern University of Science and Technology, National Center for Applied Mathematics Shenzhen, and Peng Cheng Laboratory, Shenzhen, China","institution_ids":["https://openalex.org/I3045169105","https://openalex.org/I4210136793"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100396613","display_name":"Yixuan Zhang","orcid":"https://orcid.org/0000-0002-1924-9848"},"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":"Yixuan Zhang","raw_affiliation_strings":["Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong SAR, China"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong SAR, China","institution_ids":["https://openalex.org/I14243506"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5042370642"],"corresponding_institution_ids":["https://openalex.org/I27357992"],"apc_list":null,"apc_paid":null,"fwci":2.5163,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.8883812,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"45","issue":"12","first_page":"15930","last_page":"15948"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.9986000061035156,"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/hessian-matrix","display_name":"Hessian matrix","score":0.6866703033447266},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.650139331817627},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6115224361419678},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.583490788936615},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.544960081577301},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5239603519439697},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4935957193374634},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44197404384613037},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34438228607177734},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.24133902788162231}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.6866703033447266},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.650139331817627},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6115224361419678},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.583490788936615},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.544960081577301},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5239603519439697},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4935957193374634},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44197404384613037},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34438228607177734},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.24133902788162231},{"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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.2023.3303227","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2023.3303227","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:37552592","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37552592","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on pattern analysis and machine intelligence","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1817152434","display_name":null,"funder_award_id":"U22B2052","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6695554926","display_name":null,"funder_award_id":"2022B1515020082","funder_id":"https://openalex.org/F4320337111","funder_display_name":"Basic and Applied Basic Research Foundation of Guangdong Province"},{"id":"https://openalex.org/G7041783759","display_name":null,"funder_award_id":"12222106","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320310984","display_name":"Pacific Institute for the Mathematical Sciences","ror":"https://ror.org/04w49dw51"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320337111","display_name":"Basic and Applied Basic Research Foundation of Guangdong Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W60686164","https://openalex.org/W1601741115","https://openalex.org/W1983644172","https://openalex.org/W1998288832","https://openalex.org/W2011716365","https://openalex.org/W2023858465","https://openalex.org/W2028130620","https://openalex.org/W2061924268","https://openalex.org/W2076134677","https://openalex.org/W2078101422","https://openalex.org/W2194321275","https://openalex.org/W2914953695","https://openalex.org/W2949956859","https://openalex.org/W2962770929","https://openalex.org/W2972830778","https://openalex.org/W2978409868","https://openalex.org/W2980342893","https://openalex.org/W2981748264","https://openalex.org/W2987161199","https://openalex.org/W2998993395","https://openalex.org/W3005606011","https://openalex.org/W3035486430","https://openalex.org/W3093479138","https://openalex.org/W3101372274","https://openalex.org/W3110670586","https://openalex.org/W3123350987","https://openalex.org/W3126652544","https://openalex.org/W3215151450","https://openalex.org/W4205293988","https://openalex.org/W4231147659","https://openalex.org/W4254106911","https://openalex.org/W4292230442","https://openalex.org/W4293320219","https://openalex.org/W4293867591","https://openalex.org/W4295845604","https://openalex.org/W4319653762","https://openalex.org/W6639506587","https://openalex.org/W6693919493","https://openalex.org/W6727474214","https://openalex.org/W6729767818","https://openalex.org/W6734265508","https://openalex.org/W6741832134","https://openalex.org/W6751797489","https://openalex.org/W6752515464","https://openalex.org/W6755905128","https://openalex.org/W6757297395","https://openalex.org/W6767019922","https://openalex.org/W6767599400","https://openalex.org/W6767994309","https://openalex.org/W6769066991","https://openalex.org/W6770070843","https://openalex.org/W6779138978","https://openalex.org/W6780106526","https://openalex.org/W6790260372","https://openalex.org/W6796849125","https://openalex.org/W6804528940","https://openalex.org/W6849182896"],"related_works":["https://openalex.org/W2611031068","https://openalex.org/W1704347466","https://openalex.org/W4283017538","https://openalex.org/W1996936972","https://openalex.org/W1545275724","https://openalex.org/W2802707792","https://openalex.org/W2075777916","https://openalex.org/W3021699548","https://openalex.org/W2569979269","https://openalex.org/W4297883503"],"abstract_inverted_index":{"Gradient-based":[0],"Bi-Level":[1],"Optimization":[2],"(BLO)":[3],"methods":[4,44],"have":[5],"been":[6,141],"widely":[7],"applied":[8],"to":[9,46,83,120],"handle":[10],"modern":[11],"learning":[12],"tasks.":[13,37,115],"However,":[14],"most":[15],"existing":[16,109],"strategies":[17],"are":[18,40],"theoretically":[19],"designed":[20],"based":[21],"on":[22,154,205],"restrictive":[23,162],"assumptions":[24],"(e.g.,":[25,185],"convexity":[26,164],"of":[27,93,101,152,157,183],"the":[28,85,134,149,161,174,198],"lower-level":[29,163],"sub-problem),":[30],"and":[31,59,96,104,188,201],"computationally":[32],"not":[33],"applicable":[34],"for":[35,113,133],"high-dimensional":[36,114],"Moreover,":[38],"there":[39],"almost":[41],"no":[42],"gradient-based":[43,176],"able":[45],"solve":[47,180],"BLO":[48,55,67,122,184],"in":[49,159],"those":[50],"challenging":[51,135],"scenarios,":[52],"such":[53],"as":[54],"with":[56,123,189,191],"functional":[57,125],"constraints":[58],"pessimistic":[60,136],"BLO.":[61],"In":[62,145],"this":[63,172],"work,":[64],"by":[65,108],"reformulating":[66],"into":[68],"approximated":[69],"single-level":[70],"problems,":[71],"we":[72,147],"provide":[73],"a":[74,91],"new":[75],"algorithm,":[76],"named":[77],"Bi-level":[78],"Value-Function-based":[79],"Sequential":[80],"Minimization":[81],"(BVFSM),":[82],"address":[84,121],"above":[86],"issues.":[87],"Specifically,":[88],"BVFSM":[89,119,129,153],"constructs":[90],"series":[92],"value-function-based":[94],"approximations,":[95],"thus":[97],"avoids":[98],"repeated":[99],"calculations":[100],"recurrent":[102],"gradient":[103],"Hessian":[105],"inverse":[106],"required":[107],"approaches,":[110],"time-consuming":[111],"especially":[112],"We":[116],"also":[117],"extend":[118],"additional":[124],"constraints.":[126],"More":[127],"importantly,":[128],"can":[130,179],"be":[131],"used":[132],"BLO,":[137,158],"which":[138,160],"has":[139],"never":[140],"properly":[142],"solved":[143],"before.":[144],"theory,":[146],"prove":[148],"asymptotic":[150],"convergence":[151,193],"these":[155],"types":[156],"assumption":[165],"is":[166,173],"discarded.":[167],"To":[168],"our":[169,203],"best":[170],"knowledge,":[171],"first":[175],"algorithm":[177],"that":[178],"different":[181],"kinds":[182],"optimistic,":[186],"pessimistic,":[187],"constraints)":[190],"solid":[192],"guarantees.":[194],"Extensive":[195],"experiments":[196],"verify":[197],"theoretical":[199],"investigations":[200],"demonstrate":[202],"superiority":[204],"various":[206],"real-world":[207],"applications.":[208]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2026-04-12T07:58:50.170612","created_date":"2025-10-10T00:00:00"}