{"id":"https://openalex.org/W6963263572","doi":"https://doi.org/10.17615/2qff-7702","title":"Efficient and Provable Algorithms for Convex Optimization Problems Beyond Lipschitz Continuous Gradients","display_name":"Efficient and Provable Algorithms for Convex Optimization Problems Beyond Lipschitz Continuous Gradients","publication_year":2022,"publication_date":"2022-09-13","ids":{"openalex":"https://openalex.org/W6963263572","doi":"https://doi.org/10.17615/2qff-7702"},"language":"en","primary_location":{"id":"doi:10.17615/2qff-7702","is_oa":true,"landing_page_url":"https://doi.org/10.17615/2qff-7702","pdf_url":null,"source":{"id":"https://openalex.org/S7407051488","display_name":"UNC Libraries","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"thesis"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.17615/2qff-7702","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"liu, deyi","orcid":null},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"liu, deyi","raw_affiliation_strings":["University of North Carolina at Chapel Hill"],"affiliations":[{"raw_affiliation_string":"University of North Carolina at Chapel Hill","institution_ids":["https://openalex.org/I114027177"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I114027177"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.32106715,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.642799973487854,"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"}},"topics":[{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.642799973487854,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.26190000772476196,"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.023800000548362732,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.7340999841690063},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.49140000343322754},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.43779999017715454},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4171000123023987},{"id":"https://openalex.org/keywords/exploit","display_name":"Exploit","score":0.4156999886035919},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4146000146865845},{"id":"https://openalex.org/keywords/proximal-gradient-methods-for-learning","display_name":"Proximal gradient methods for learning","score":0.41029998660087585},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.4027999937534332},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.38749998807907104}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7340999841690063},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.60589998960495},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5659999847412109},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.49140000343322754},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.43779999017715454},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4171000123023987},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.4156999886035919},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41519999504089355},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4146000146865845},{"id":"https://openalex.org/C79248915","wikidata":"https://www.wikidata.org/wiki/Q17086776","display_name":"Proximal gradient methods for learning","level":5,"score":0.41029998660087585},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.4027999937534332},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.38749998807907104},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.37860000133514404},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.375},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.3668000102043152},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.36469998955726624},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.35760000348091125},{"id":"https://openalex.org/C122268817","wikidata":"https://www.wikidata.org/wiki/Q2020318","display_name":"Frank\u2013Wolfe algorithm","level":5,"score":0.3560999929904938},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3521000146865845},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.34040001034736633},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.32120001316070557},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.3043999969959259},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.3025999963283539},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.2921999990940094},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.27129998803138733},{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.2660999894142151}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.17615/2qff-7702","is_oa":true,"landing_page_url":"https://doi.org/10.17615/2qff-7702","pdf_url":null,"source":{"id":"https://openalex.org/S7407051488","display_name":"UNC Libraries","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"thesis"}],"best_oa_location":{"id":"doi:10.17615/2qff-7702","is_oa":true,"landing_page_url":"https://doi.org/10.17615/2qff-7702","pdf_url":null,"source":{"id":"https://openalex.org/S7407051488","display_name":"UNC Libraries","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"thesis"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0,51,159],"thesis":[1,160],"aims":[2],"at":[3],"developing":[4],"efficient":[5,149,416],"algorithms":[6,150],"for":[7,151,185,420],"solving":[8],"complex":[9],"and":[10,46,76,81,94,114,145,148,173,198,283,304,316,331,389,399],"constrained":[11,189,252],"convex":[12,104,153,340],"optimization":[13,67],"problems":[14,154],"with":[15,127,155],"provable":[16],"convergence":[17,370],"guarantees.":[18],"Unlike":[19,343],"existing":[20,344],"methods":[21,59,200],"which":[22,107,273,346],"heavily":[23],"rely":[24,347],"on":[25,348],"the":[26,30,33,39,49,128,132,141,168,171,196,203,209,216,226,231,235,266,270,286,291,297,302,326,354,375,380,385,391],"Lipschitz":[27,142],"continuity":[28],"of":[29,32,41,131,162,188,208,218,221,230,285,313,351,353],"gradient":[31,143,329],"objective":[34,133],"function,":[35],"we":[36,120,194,239,307,324,357,395],"instead":[37,358],"exploit":[38,202],"notion":[40],"self-concordance":[42],"introduced":[43],"by":[44],"Nesterov":[45],"Nemirovskii":[47],"in":[48,57,65,79,102,111,234,256,300,321,384,405],"1990s.":[50],"concept":[52],"has":[53,61],"been":[54,63],"intensively":[55],"used":[56,110],"interior-point":[58,244],"but":[60],"recently":[62],"exploited":[64],"other":[66],"schemes.":[68],"In":[69,117],"addition,":[70],"self-concordant":[71,190],"functions":[72],"cover":[73],"many":[74],"new":[75,181,242],"prominent":[77],"applications":[78],"statistics":[80],"machine":[82,112],"learning,":[83],"such":[84],"as":[85,228],"inverse":[86],"covariance-type":[87],"estimation,":[88],"regularized":[89],"logistic":[90],"regression,":[91],"portfolio":[92],"optimization,":[93],"optimal":[95],"experimental":[96],"design.":[97],"We":[98,212,372],"are":[99,108,175],"also":[100],"interested":[101],"nonsmooth":[103,129,339,355],"composite":[105,253,341],"problems,":[106,192,306],"widely":[109],"learning":[113],"image":[115],"processing.":[116],"this":[118],"setting,":[119],"utilize":[121],"Nesterov's":[122,332],"smoothing":[123,333,364,382,417],"technique":[124,334,378],"to":[125,138,201,248,263,275,335,366,379,413],"deal":[126],"part":[130],"function.":[134],"Our":[135,259,408],"approach":[136],"is":[137,167,224,412],"go":[139],"beyond":[140],"structure":[144],"develop":[146,414],"novel":[147],"different":[152],"polynomial-time":[156,311],"iteration":[157],"complexity.":[158,393],"consists":[161],"five":[163],"chapters.":[164],"Chapter":[165,177,257,322,406],"1":[166],"introduction,":[169],"where":[170,193],"motivation":[172],"background":[174],"presented.":[176],"2":[178],"develops":[179],"a":[180,186,241,250,310,337,368],"Newton":[182,197],"Frank-Wolfe":[183,199,232],"algorithm":[184,315,419],"class":[187],"minimization":[191,205,254],"combine":[195,325],"linear":[204],"oracles":[206,277],"(LMO)":[207],"feasible":[210],"set.":[211],"theoretically":[213],"prove":[214],"that":[215,229],"number":[217],"LMO":[219],"calls":[220],"our":[222,314,397],"method":[223,233,247,260,330,383],"nearly":[225],"same":[227],"L-smooth":[236],"case.":[237],"Next,":[238],"propose":[240],"inexact":[243,276,279,298],"Lagrangian":[245],"decomposition":[246],"solve":[249,265,336],"general":[251],"problem":[255,289],"3.":[258],"allows":[261],"one":[262],"approximately":[264],"primal":[267,318],"subproblems":[268],"(called":[269,290],"slave":[271,303],"problems),":[272],"leads":[274],"(i.e.,":[278],"function":[280],"value,":[281],"gradient,":[282],"Hessian)":[284],"smoothed":[287],"dual":[288],"master":[292,305],"problem).":[293],"By":[294],"appropriately":[295],"controlling":[296],"computation":[299],"both":[301],"can":[308],"establish":[309],"iteration-complexity":[312],"recover":[317],"solutions.":[319],"Then,":[320],"4,":[323],"accelerated":[327],"stochastic":[328,338,418,422],"problem.":[342],"works,":[345],"unbiased":[349],"estimators":[350],"subgradients":[352],"term,":[356],"explore":[359],"its":[360],"proximal":[361],"operator":[362],"via":[363],"techniques":[365],"obtain":[367],"better":[369],"rate.":[371],"further":[373],"adapt":[374],"variance":[376],"reduction":[377],"proposed":[381],"finite":[386],"sum":[387],"case":[388],"achieve":[390],"best-known":[392],"Finally,":[394],"summarize":[396],"contribution":[398],"outline":[400],"some":[401],"future":[402,409],"research":[403,410],"directions":[404],"5.":[407],"plan":[411],"an":[415],"two-stage":[421],"programming.":[423]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}
