{"id":"https://openalex.org/W3131236130","doi":"https://doi.org/10.1109/tpami.2021.3059301","title":"The fastest L1,oo prox in the west","display_name":"The fastest L1,oo prox in the west","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3131236130","doi":"https://doi.org/10.1109/tpami.2021.3059301","mag":"3131236130","pmid":"https://pubmed.ncbi.nlm.nih.gov/33587698"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2021.3059301","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2021.3059301","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/A5058720464","display_name":"Benjam\u0131\u0301n B\u00e9jar","orcid":"https://orcid.org/0000-0001-9705-4483"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]},{"id":"https://openalex.org/I4210122261","display_name":"Swiss Data Science Center","ror":"https://ror.org/02hdt9m26","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I2799323385","https://openalex.org/I35440088","https://openalex.org/I4210122261","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Benjamin Bejar","raw_affiliation_strings":["Swiss Data Science Center, EPFL, 27218 Lausanne, VD, Switzerland, (e-mail: bbejar@cis.jhu.edu)"],"affiliations":[{"raw_affiliation_string":"Swiss Data Science Center, EPFL, 27218 Lausanne, VD, Switzerland, (e-mail: bbejar@cis.jhu.edu)","institution_ids":["https://openalex.org/I4210122261","https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002015062","display_name":"Ivan Dokmani\u0107","orcid":"https://orcid.org/0000-0001-7132-5214"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ivan Dokmanic","raw_affiliation_strings":["ECE, University of Illinois at Urbana-Champaign, Urbana, Illinois, United States, (e-mail: dokmanic@illinois.edu)","[ECE, University of Illinois at Urbana-Champaign, Urbana, Illinois, United States, (e-mail: dokmanic@illinois.edu)]"],"affiliations":[{"raw_affiliation_string":"ECE, University of Illinois at Urbana-Champaign, Urbana, Illinois, United States, (e-mail: dokmanic@illinois.edu)","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"[ECE, University of Illinois at Urbana-Champaign, Urbana, Illinois, United States, (e-mail: dokmanic@illinois.edu)]","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011256828","display_name":"Ren\u00e8 Vidal","orcid":"https://orcid.org/0000-0003-1838-0761"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rene Vidal","raw_affiliation_strings":["Biomedical Engineering, Johns Hopkins University - Homewood Campus, 1466 Baltimore, Maryland, United States, (e-mail: rvidal@jhu.edu)"],"affiliations":[{"raw_affiliation_string":"Biomedical Engineering, Johns Hopkins University - Homewood Campus, 1466 Baltimore, Maryland, United States, (e-mail: rvidal@jhu.edu)","institution_ids":["https://openalex.org/I145311948"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5058720464"],"corresponding_institution_ids":["https://openalex.org/I4210122261","https://openalex.org/I5124864"],"apc_list":null,"apc_paid":null,"fwci":0.3502,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.51388889,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"44","issue":"7","first_page":"1","last_page":"1"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9994999766349792,"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":0.9994999766349792,"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/T12303","display_name":"Tensor decomposition and applications","score":0.992900013923645,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9896000027656555,"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/matrix-norm","display_name":"Matrix norm","score":0.6125462055206299},{"id":"https://openalex.org/keywords/thresholding","display_name":"Thresholding","score":0.6052347421646118},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5612446069717407},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5342060327529907},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5312753915786743},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5048044919967651},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5003025531768799},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.49998044967651367},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4685296416282654},{"id":"https://openalex.org/keywords/operator-norm","display_name":"Operator norm","score":0.43084388971328735},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3883969187736511},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1978445053100586},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.1619671881198883},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.13991603255271912},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.12394446134567261},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.0852227509021759}],"concepts":[{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.6125462055206299},{"id":"https://openalex.org/C191178318","wikidata":"https://www.wikidata.org/wiki/Q2256906","display_name":"Thresholding","level":3,"score":0.6052347421646118},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5612446069717407},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5342060327529907},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5312753915786743},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5048044919967651},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5003025531768799},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49998044967651367},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4685296416282654},{"id":"https://openalex.org/C68386474","wikidata":"https://www.wikidata.org/wiki/Q980557","display_name":"Operator norm","level":3,"score":0.43084388971328735},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3883969187736511},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1978445053100586},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.1619671881198883},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.13991603255271912},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.12394446134567261},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0852227509021759},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.2021.3059301","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2021.3059301","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:33587698","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33587698","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/G8126959550","display_name":null,"funder_award_id":"NSF 1704458","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1551136530","https://openalex.org/W1945589809","https://openalex.org/W1946620893","https://openalex.org/W1953936588","https://openalex.org/W1966872876","https://openalex.org/W1978259121","https://openalex.org/W2045220410","https://openalex.org/W2047092297","https://openalex.org/W2056385679","https://openalex.org/W2089749945","https://openalex.org/W2097413644","https://openalex.org/W2102412823","https://openalex.org/W2149954962","https://openalex.org/W2157531738","https://openalex.org/W2159400887","https://openalex.org/W2159514083","https://openalex.org/W2180180824","https://openalex.org/W2653474537","https://openalex.org/W2810681346","https://openalex.org/W2897477974","https://openalex.org/W4205213118","https://openalex.org/W4244393449","https://openalex.org/W4250589301","https://openalex.org/W4301014524","https://openalex.org/W6632976901","https://openalex.org/W6682191629","https://openalex.org/W6683157813","https://openalex.org/W6683546621"],"related_works":["https://openalex.org/W2374649169","https://openalex.org/W2023111059","https://openalex.org/W2101854716","https://openalex.org/W3184166521","https://openalex.org/W3100870169","https://openalex.org/W4386164526","https://openalex.org/W1664553927","https://openalex.org/W2158044763","https://openalex.org/W2166259197","https://openalex.org/W2492152744"],"abstract_inverted_index":{"Proximal":[0],"operators":[1],"are":[2],"of":[3,41,61,86,109,153,172],"particular":[4],"interest":[5],"in":[6,14,28,74,101],"optimization":[7,21],"problems":[8],"dealing":[9],"with":[10],"non-smooth":[11],"objectives":[12],"because":[13],"many":[15],"practical":[16],"cases":[17],"they":[18],"lead":[19],"to":[20,83,145],"algorithms":[22],"whose":[23],"updates":[24],"can":[25,71,169],"be":[26,72,170],"computed":[27,73],"closed":[29,75],"form":[30,76],"or":[31],"very":[32],"efficiently.":[33],"A":[34],"well-known":[35,80],"example":[36],"is":[37,47,99],"the":[38,42,50,58,62,79,87,91,97,102,110,122,150,154,166],"proximal":[39,59],"operator":[40,60,82],"vector":[43,92],"l<sub>1</sub>":[44,93],"norm,":[45],"which":[46],"given":[48,123],"by":[49,77],"soft-thresholding":[51,81],"operator.":[52],"In":[53],"this":[54],"paper":[55],"we":[56],"study":[57],"mixed":[63,103,151],"l<sub>1,\u221e</sub>":[64,104],"matrix":[65,111],"norm":[66,94,105,152],"and":[67,117,161],"show":[68],"that":[69,141,165],"it":[70],"applying":[78],"each":[84,107],"column":[85,108],"matrix.":[88,124],"However,":[89],"unlike":[90],"case":[95,106],"where":[96],"threshold":[98,116],"constant,":[100],"might":[112],"require":[113],"a":[114,127],"different":[115],"all":[118],"thresholds":[119],"depend":[120],"on":[121,158],"We":[125],"propose":[126],"general":[128],"iterative":[129],"algorithm":[130],"for":[131,149],"computing":[132],"these":[133],"thresholds,":[134],"as":[135,137],"well":[136],"two":[138],"efficient":[139],"implementations":[140],"further":[142],"exploit":[143],"easy":[144],"compute":[146],"lower":[147],"bounds":[148],"optimal":[155],"solution.":[156],"Experiments":[157],"large-scale":[159],"synthetic":[160],"real":[162],"data":[163],"indicate":[164],"proposed":[167],"methods":[168],"orders":[171],"magnitude":[173],"faster":[174],"than":[175],"state-of-the-art":[176],"methods.":[177]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2021-03-01T00:00:00"}