{"id":"https://openalex.org/W2019786292","doi":"https://doi.org/10.1137/110844805","title":"Accelerated and Inexact Forward-Backward Algorithms","display_name":"Accelerated and Inexact Forward-Backward Algorithms","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2019786292","doi":"https://doi.org/10.1137/110844805","mag":"2019786292"},"language":"en","primary_location":{"id":"doi:10.1137/110844805","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110844805","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":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/190939","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053468228","display_name":"Silvia Villa","orcid":"https://orcid.org/0000-0002-6232-5631"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Silvia Villa","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017463552","display_name":"Saverio Salzo","orcid":"https://orcid.org/0000-0003-0494-9101"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Saverio Salzo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026055401","display_name":"Luca Baldassarre","orcid":"https://orcid.org/0000-0002-8050-2048"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luca Baldassarre","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5036620304","display_name":"Alessandro Verri","orcid":"https://orcid.org/0000-0001-9777-9986"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alessandro Verri","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":15.7787,"has_fulltext":false,"cited_by_count":198,"citation_normalized_percentile":{"value":0.99491268,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"23","issue":"3","first_page":"1607","last_page":"1633"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9995999932289124,"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":0.9995999932289124,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9879999756813049,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7786703109741211},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6406567096710205},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6295838356018066},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.6022637486457825},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5618919730186462},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5502630472183228},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5279877781867981},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.46032774448394775},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.4195369482040405},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4176263213157654},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38957467675209045},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3848884403705597},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1892695426940918},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.11532631516456604},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.0688847005367279}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7786703109741211},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6406567096710205},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6295838356018066},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.6022637486457825},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5618919730186462},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5502630472183228},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5279877781867981},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.46032774448394775},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.4195369482040405},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4176263213157654},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38957467675209045},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3848884403705597},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1892695426940918},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.11532631516456604},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.0688847005367279},{"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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","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},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/110844805","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110844805","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:CiteSeerX.psu:10.1.1.416.3633","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.416.3633","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.optimization-online.org/DB_FILE/2011/08/3132.pdf","raw_type":"text"},{"id":"pmh:oai:infoscience.epfl.ch:190939","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/190939","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:infoscience.tind.io:190939","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/97561","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"research article"},{"id":"pmh:oai:iris.unige.it:11567/698769","is_oa":false,"landing_page_url":"http://hdl.handle.net/11567/698769","pdf_url":null,"source":{"id":"https://openalex.org/S4377196291","display_name":"CINECA IRIS Institutial Research Information System (University of Genoa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I83816512","host_organization_name":"University of Genoa","host_organization_lineage":["https://openalex.org/I83816512"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:iris.uniroma1.it:11573/1654464","is_oa":false,"landing_page_url":"http://hdl.handle.net/11573/1654464","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:190939","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/190939","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":84,"referenced_works":["https://openalex.org/W109372583","https://openalex.org/W163258351","https://openalex.org/W202170286","https://openalex.org/W595086808","https://openalex.org/W1043777763","https://openalex.org/W1494951781","https://openalex.org/W1505731132","https://openalex.org/W1544177383","https://openalex.org/W1553702074","https://openalex.org/W1568288633","https://openalex.org/W1575261714","https://openalex.org/W1646506067","https://openalex.org/W1886579186","https://openalex.org/W1946620893","https://openalex.org/W1953936588","https://openalex.org/W1970554427","https://openalex.org/W1981112674","https://openalex.org/W1981798752","https://openalex.org/W1982011875","https://openalex.org/W1993531186","https://openalex.org/W1994309289","https://openalex.org/W1998576973","https://openalex.org/W2000594266","https://openalex.org/W2005089986","https://openalex.org/W2006262045","https://openalex.org/W2018056315","https://openalex.org/W2019569173","https://openalex.org/W2023722580","https://openalex.org/W2037679050","https://openalex.org/W2038497950","https://openalex.org/W2039466093","https://openalex.org/W2039939700","https://openalex.org/W2043093325","https://openalex.org/W2052432211","https://openalex.org/W2079491734","https://openalex.org/W2083432309","https://openalex.org/W2084777452","https://openalex.org/W2092663520","https://openalex.org/W2093545205","https://openalex.org/W2094097069","https://openalex.org/W2099679613","https://openalex.org/W2100556411","https://openalex.org/W2101868363","https://openalex.org/W2103559027","https://openalex.org/W2107602185","https://openalex.org/W2108687351","https://openalex.org/W2109449402","https://openalex.org/W2114605231","https://openalex.org/W2118429861","https://openalex.org/W2122890444","https://openalex.org/W2124125796","https://openalex.org/W2124541940","https://openalex.org/W2124682210","https://openalex.org/W2124768887","https://openalex.org/W2126976013","https://openalex.org/W2129284024","https://openalex.org/W2130410032","https://openalex.org/W2130698040","https://openalex.org/W2135779729","https://openalex.org/W2137080665","https://openalex.org/W2138019504","https://openalex.org/W2138216979","https://openalex.org/W2140514146","https://openalex.org/W2142224912","https://openalex.org/W2145003640","https://openalex.org/W2149726258","https://openalex.org/W2156074207","https://openalex.org/W2158065297","https://openalex.org/W2160450758","https://openalex.org/W2164224215","https://openalex.org/W2164301055","https://openalex.org/W2166407369","https://openalex.org/W2338175496","https://openalex.org/W2604272474","https://openalex.org/W2765202580","https://openalex.org/W2952975724","https://openalex.org/W2969945254","https://openalex.org/W3029645440","https://openalex.org/W3099503819","https://openalex.org/W3104579394","https://openalex.org/W3124114587","https://openalex.org/W3183134511","https://openalex.org/W4205213118","https://openalex.org/W4244208880"],"related_works":["https://openalex.org/W2015327483","https://openalex.org/W1678820847","https://openalex.org/W2559216629","https://openalex.org/W2037211941","https://openalex.org/W4298096494","https://openalex.org/W1553684505","https://openalex.org/W1998295157","https://openalex.org/W2015288657","https://openalex.org/W4297883503","https://openalex.org/W3149331067"],"abstract_inverted_index":{"We":[0,34],"propose":[1],"a":[2,31,54,59,89],"convergence":[3,39],"analysis":[4,65,108],"of":[5,53,71,81,98,102],"accelerated":[6,82],"forward-backward":[7],"splitting":[8],"methods":[9],"for":[10,41,78],"composite":[11],"function":[12,43],"minimization,":[13],"when":[14],"the":[15,37,42,49,69,79,96,103],"proximity":[16],"operator":[17],"is":[18,66,109],"not":[19],"available":[20],"in":[21],"closed":[22],"form,":[23],"and":[24,57],"can":[25,45],"only":[26],"be":[27,46],"computed":[28],"up":[29],"to":[30],"certain":[32,55],"precision.":[33],"prove":[35],"that":[36],"$1/k^2$":[38],"rate":[40],"values":[44],"achieved":[47],"if":[48],"admissible":[50,100],"errors":[51],"are":[52],"type":[56],"satisfy":[58],"sufficiently":[60],"fast":[61],"decay":[62],"condition.":[63],"Our":[64],"based":[67],"on":[68],"machinery":[70],"estimate":[72],"sequences":[73],"first":[74],"introduced":[75],"by":[76],"Nesterov":[77],"study":[80],"gradient":[83],"descent":[84],"algorithms.":[85],"Furthermore,":[86],"we":[87],"give":[88],"global":[90],"complexity":[91],"analysis,":[92],"taking":[93],"into":[94],"account":[95],"cost":[97],"computing":[99],"approximations":[101],"proximal":[104],"point.":[105],"An":[106],"experimental":[107],"also":[110],"presented.":[111]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":27},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":18},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":15},{"year":2018,"cited_by_count":18},{"year":2017,"cited_by_count":17},{"year":2016,"cited_by_count":19},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
