{"id":"https://openalex.org/W2908439849","doi":"https://doi.org/10.1137/19m1240460","title":"Generalized Conditional Gradient with Augmented Lagrangian for Composite Minimization","display_name":"Generalized Conditional Gradient with Augmented Lagrangian for Composite Minimization","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2908439849","doi":"https://doi.org/10.1137/19m1240460","mag":"2908439849"},"language":"en","primary_location":{"id":"doi:10.1137/19m1240460","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1240460","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1901.01287","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080907074","display_name":"Antonio Silveti-Falls","orcid":"https://orcid.org/0000-0002-8165-6348"},"institutions":[{"id":"https://openalex.org/I4210139483","display_name":"GREYC","ror":"https://ror.org/043749971","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I194210350","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210139483","https://openalex.org/I4210159245","https://openalex.org/I98702875"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Antonio Silveti-Falls","raw_affiliation_strings":["Equipe Image - Laboratoire GREYC - UMR6072 (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Equipe Image - Laboratoire GREYC - UMR6072 (France)","institution_ids":["https://openalex.org/I4210139483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041695668","display_name":"Cesare Molinari","orcid":"https://orcid.org/0000-0003-0864-5682"},"institutions":[{"id":"https://openalex.org/I4210139483","display_name":"GREYC","ror":"https://ror.org/043749971","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I194210350","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210139483","https://openalex.org/I4210159245","https://openalex.org/I98702875"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Cesare Molinari","raw_affiliation_strings":["Equipe Image - Laboratoire GREYC - UMR6072 (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Equipe Image - Laboratoire GREYC - UMR6072 (France)","institution_ids":["https://openalex.org/I4210139483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008136365","display_name":"Jalal Fadili","orcid":"https://orcid.org/0000-0002-8165-7578"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210105918","display_name":"Normandie Universit\u00e9","ror":"https://ror.org/01k40cz91","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918"]},{"id":"https://openalex.org/I4210139483","display_name":"GREYC","ror":"https://ror.org/043749971","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I194210350","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210139483","https://openalex.org/I4210159245","https://openalex.org/I98702875"]},{"id":"https://openalex.org/I98702875","display_name":"Universit\u00e9 de Caen Normandie","ror":"https://ror.org/051kpcy16","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I98702875"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jalal Fadili","raw_affiliation_strings":["Normandie Universit\u00e9, ENSICAEN, UNICAEN, CNRS, GREYC, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Normandie Universit\u00e9, ENSICAEN, UNICAEN, CNRS, GREYC, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210105918","https://openalex.org/I4210139483","https://openalex.org/I98702875"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0018,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.6786544,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"30","issue":"4","first_page":"2687","last_page":"2725"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9987999796867371,"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":0.9987999796867371,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9977999925613403,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9955000281333923,"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/mathematics","display_name":"Mathematics","score":0.8306280374526978},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6424760818481445},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6049202680587769},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6009970307350159},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.569699764251709},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4860013425350189},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4829844534397125},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.4600865840911865},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.4412708878517151},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25799959897994995},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19045814871788025}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8306280374526978},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6424760818481445},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6049202680587769},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6009970307350159},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.569699764251709},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4860013425350189},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4829844534397125},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.4600865840911865},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.4412708878517151},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25799959897994995},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19045814871788025},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/19m1240460","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1240460","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1901.01287","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1901.01287","pdf_url":"https://arxiv.org/pdf/1901.01287","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:HAL:hal-02307114v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02307114","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Optimization, In press, 30 (4), pp.2687-2725. ⟨10.1137/19M1240460⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1901.01287","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1901.01287","pdf_url":"https://arxiv.org/pdf/1901.01287","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321778","display_name":"Conseil R\u00e9gional de Haute Normandie","ror":"https://ror.org/03w805n83"},{"id":"https://openalex.org/F4320322893","display_name":"Institut Universitaire de France","ror":"https://ror.org/055khg266"},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W905619","https://openalex.org/W27352379","https://openalex.org/W205960364","https://openalex.org/W597610935","https://openalex.org/W1517403807","https://openalex.org/W1574851760","https://openalex.org/W1585386565","https://openalex.org/W1855169650","https://openalex.org/W1966905102","https://openalex.org/W1969244384","https://openalex.org/W1975490585","https://openalex.org/W1985240368","https://openalex.org/W1994569450","https://openalex.org/W2003146967","https://openalex.org/W2013243898","https://openalex.org/W2030254567","https://openalex.org/W2040676043","https://openalex.org/W2052551315","https://openalex.org/W2053487511","https://openalex.org/W2061657011","https://openalex.org/W2074494226","https://openalex.org/W2097717989","https://openalex.org/W2105864171","https://openalex.org/W2121133091","https://openalex.org/W2136106887","https://openalex.org/W2136885855","https://openalex.org/W2140180727","https://openalex.org/W2172790076","https://openalex.org/W2551153860","https://openalex.org/W2602335281","https://openalex.org/W2765442055","https://openalex.org/W2782341585","https://openalex.org/W2797899988","https://openalex.org/W2798458649","https://openalex.org/W2798635843","https://openalex.org/W2949605370","https://openalex.org/W2962827308","https://openalex.org/W2964177174","https://openalex.org/W3021722416","https://openalex.org/W3106503251","https://openalex.org/W3166476363","https://openalex.org/W4229650096","https://openalex.org/W4299989987"],"related_works":["https://openalex.org/W1677518548","https://openalex.org/W4286857066","https://openalex.org/W3213958552","https://openalex.org/W4238239967","https://openalex.org/W4297812081","https://openalex.org/W2949926331","https://openalex.org/W2754545762","https://openalex.org/W4299562540","https://openalex.org/W3175273680","https://openalex.org/W4298208753"],"abstract_inverted_index":{"In":[0,168],"this":[1,170],"paper":[2],"we":[3,20,120,150,228],"propose":[4],"a":[5,15,66,161,181,211],"splitting":[6],"scheme":[7],"which":[8,19],"hybridizes":[9],"the":[10,22,27,70,84,87,91,104,113,118,137,145,178,195,201,235,241,247,251,266,270],"generalized":[11],"conditional":[12,77],"gradient":[13,78,85],"with":[14,55,191,232],"proximal":[16,139],"step":[17],"and":[18,33,101,159,244,259,269],"call":[21],"CGALP":[23,93],"algorithm":[24,215],"for":[25,210,264],"minimizing":[26],"sum":[28,59],"of":[29,60,83,86,90,107,110,180,214,240,246,262],"three":[30,63],"proper":[31],"convex":[32,185],"lower-semicontinuous":[34],"functions":[35,116],"in":[36,49,65,117,187],"real":[37],"Hilbert":[38],"spaces.":[39],"The":[40,128],"minimization":[41,164],"is":[42,133,141,156,166,198,207],"subject":[43],"to":[44,53,176,189,234,250],"an":[45,98],"affine":[46,196,236],"constraint,":[47,237],"that,":[48],"particular,":[50,169],"allows":[51],"one":[52],"deal":[54,190],"composite":[56],"problems":[57],"(a":[58],"more":[61],"than":[62],"functions)":[64],"separable":[67],"way":[68],"by":[69,200],"usual":[71],"product":[72],"space":[73],"technique.":[74],"While":[75],"classical":[76],"methods":[79],"require":[80,123],"Lipschitz":[81,108],"continuity":[82,109],"differentiable":[88],"part":[89],"objective,":[92,119],"needs":[94],"only":[95],"differentiability":[96],"(on":[97],"appropriate":[99],"subset)":[100],"hence":[102],"circumvents":[103],"intricate":[105],"question":[106],"gradients.":[111],"For":[112,144],"two":[114],"remaining":[115],"do":[121],"not":[122],"any":[124],"additional":[125,192],"regularity":[126],"assumption.":[127],"second":[129],"function,":[130,147],"possibly":[131],"nonsmooth,":[132,149],"assumed":[134],"simple;":[135],"i.e.,":[136],"associated":[138],"mapping":[140],"easily":[142],"computable.":[143],"third":[146],"again":[148],"just":[151],"assume":[152],"that":[153,160],"its":[154],"domain":[155],"weakly":[157],"compact":[158],"linearly":[162],"perturbed":[163],"oracle":[165],"accessible.":[167],"last":[171],"function":[172],"can":[173],"be":[174,177],"chosen":[175],"indicator":[179],"nonempty":[182],"bounded":[183],"closed":[184],"set":[186],"order":[188],"constraints.":[193],"Finally,":[194],"constraint":[197],"addressed":[199],"augmented":[202],"Lagrangian":[203,248,271],"approach.":[204],"Our":[205],"analysis":[206],"carried":[208],"out":[209],"wide":[212],"choice":[213],"parameters":[216],"satisfying":[217],"so-called":[218],"open":[219],"loop":[220],"rules.":[221],"As":[222],"main":[223],"results,":[224],"under":[225],"mild":[226],"conditions,":[227],"show":[229],"asymptotic":[230],"feasibility":[231,267],"respect":[233],"weak":[238],"convergence":[239,245,263],"dual":[242],"multipliers,":[243],"values":[249],"saddle-point":[252],"optimal":[253],"value.":[254],"We":[255],"also":[256],"provide":[257],"pointwise":[258],"ergodic":[260],"rates":[261],"both":[265],"gap":[268],"values.":[272]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}