{"id":"https://openalex.org/W4379880290","doi":"https://doi.org/10.1080/10556788.2023.2212503","title":"Accelerated gradient methods with absolute and relative noise in the gradient","display_name":"Accelerated gradient methods with absolute and relative noise in the gradient","publication_year":2023,"publication_date":"2023-06-08","ids":{"openalex":"https://openalex.org/W4379880290","doi":"https://doi.org/10.1080/10556788.2023.2212503"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2023.2212503","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10556788.2023.2212503","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/10556788.2023.2212503?needAccess=true&role=button","source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.tandfonline.com/doi/pdf/10.1080/10556788.2023.2212503?needAccess=true&role=button","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088183252","display_name":"Vasin Artem","orcid":null},"institutions":[{"id":"https://openalex.org/I153845743","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322","country_code":"RU","type":"education","lineage":["https://openalex.org/I153845743"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Artem Vasin","raw_affiliation_strings":["Moscow Institute of Physics and Technology, Research Center of Applied AI Systems, Dolgoprudny, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Moscow Institute of Physics and Technology, Research Center of Applied AI Systems, Dolgoprudny, Russia","institution_ids":["https://openalex.org/I153845743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028866398","display_name":"Alexander Gasnikov","orcid":"https://orcid.org/0000-0002-7386-039X"},"institutions":[{"id":"https://openalex.org/I153845743","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322","country_code":"RU","type":"education","lineage":["https://openalex.org/I153845743"]},{"id":"https://openalex.org/I4210107660","display_name":"Institute for Information Transmission Problems","ror":"https://ror.org/013w2d378","country_code":"RU","type":"facility","lineage":["https://openalex.org/I4210107660"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Alexander Gasnikov","raw_affiliation_strings":["Institute for Information Transmission Problems, Sector 7, Moscow, Russia","Moscow Institute of Physics and Technology, Lab Mathematical Methods of Optimization, Dolgoprudny, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Information Transmission Problems, Sector 7, Moscow, Russia","institution_ids":["https://openalex.org/I4210107660"]},{"raw_affiliation_string":"Moscow Institute of Physics and Technology, Lab Mathematical Methods of Optimization, Dolgoprudny, Russia","institution_ids":["https://openalex.org/I153845743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082992656","display_name":"Pavel Dvurechensky","orcid":"https://orcid.org/0000-0003-1201-2343"},"institutions":[{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Pavel Dvurechensky","raw_affiliation_strings":["Weierstrass Institute for Applied Analysis and Stochastics, Research Group Stochastic Algorithms and Nonparametric Statistics, Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0003-1201-2343","affiliations":[{"raw_affiliation_string":"Weierstrass Institute for Applied Analysis and Stochastics, Research Group Stochastic Algorithms and Nonparametric Statistics, Berlin, Germany","institution_ids":["https://openalex.org/I4210092021"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035705885","display_name":"Vladimir Spokoiny","orcid":"https://orcid.org/0000-0002-2040-3427"},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]},{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Vladimir Spokoiny","raw_affiliation_strings":["Humboldt-University of Berlin, Institute of Mathematics, Berlin, Germany","Weierstrass Institute for Applied Analysis and Stochastics, Research Group Stochastic Algorithms and Nonparametric Statistics, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Humboldt-University of Berlin, Institute of Mathematics, Berlin, Germany","institution_ids":["https://openalex.org/I39343248"]},{"raw_affiliation_string":"Weierstrass Institute for Applied Analysis and Stochastics, Research Group Stochastic Algorithms and Nonparametric Statistics, Berlin, Germany","institution_ids":["https://openalex.org/I4210092021"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5082992656"],"corresponding_institution_ids":["https://openalex.org/I4210092021"],"apc_list":null,"apc_paid":null,"fwci":1.6034,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.8004371,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"38","issue":"6","first_page":"1180","last_page":"1229"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.998199999332428,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9973999857902527,"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":0.6325058341026306},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6170845627784729},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5703341364860535},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.563641369342804},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5635485053062439},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5007703304290771},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4584140479564667},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.45194533467292786},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.43053194880485535},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4167463481426239},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26592496037483215},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2599599361419678},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.07248857617378235},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06756281852722168},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06492534279823303}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6325058341026306},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6170845627784729},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5703341364860535},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.563641369342804},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5635485053062439},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5007703304290771},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4584140479564667},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.45194533467292786},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43053194880485535},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4167463481426239},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26592496037483215},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2599599361419678},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.07248857617378235},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06756281852722168},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06492534279823303},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556788.2023.2212503","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10556788.2023.2212503","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/10556788.2023.2212503?needAccess=true&role=button","source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1080/10556788.2023.2212503","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10556788.2023.2212503","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/10556788.2023.2212503?needAccess=true&role=button","source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2928192979","display_name":null,"funder_award_id":"000000D730321P5Q0002","funder_id":"https://openalex.org/F4320319755","funder_display_name":"Analytical Center for the Government of the Russian Federation"},{"id":"https://openalex.org/G5927019889","display_name":null,"funder_award_id":"70-2021-00138","funder_id":"https://openalex.org/F4320330091","funder_display_name":"Moscow Institute of Physics and Technology"}],"funders":[{"id":"https://openalex.org/F4320319755","display_name":"Analytical Center for the Government of the Russian Federation","ror":null},{"id":"https://openalex.org/F4320330091","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4379880290.pdf"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W181733065","https://openalex.org/W195619270","https://openalex.org/W1962121538","https://openalex.org/W2121210949","https://openalex.org/W2124768887","https://openalex.org/W2135472208","https://openalex.org/W2149479912","https://openalex.org/W2400216583","https://openalex.org/W2502393534","https://openalex.org/W2514921637","https://openalex.org/W2556098900","https://openalex.org/W2763081248","https://openalex.org/W2790570656","https://openalex.org/W2901838001","https://openalex.org/W2998975330","https://openalex.org/W3024063968","https://openalex.org/W3025638325","https://openalex.org/W3035736653","https://openalex.org/W3084325032","https://openalex.org/W3109064640","https://openalex.org/W3124203093","https://openalex.org/W3163478863","https://openalex.org/W3164350488","https://openalex.org/W3178749228","https://openalex.org/W3211250483","https://openalex.org/W4205547947","https://openalex.org/W4206742934","https://openalex.org/W4224990512","https://openalex.org/W4249667877","https://openalex.org/W4287757895","https://openalex.org/W4292064643","https://openalex.org/W4298293704","https://openalex.org/W4301435544"],"related_works":["https://openalex.org/W3013085049","https://openalex.org/W1560496689","https://openalex.org/W4386900933","https://openalex.org/W4385301946","https://openalex.org/W4297797135","https://openalex.org/W3125672081","https://openalex.org/W1673581201","https://openalex.org/W1793337513","https://openalex.org/W2296389180","https://openalex.org/W3153752017"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"investigate":[4,52],"accelerated":[5],"first-order":[6],"methods":[7],"for":[8,105],"smooth":[9],"convex":[10,60,63],"optimization":[11,116],"problems":[12],"under":[13],"inexact":[14],"information":[15],"on":[16,93],"the":[17,20,25,46,49,53,56,59,66,72,77,86,94,97,106,112],"gradient":[18,26],"of":[19,48,55,71,96,114],"objective.":[21],"The":[22,83],"noise":[23,36,43],"in":[24,58],"is":[27,88],"considered":[28],"to":[29,45,85,89,111],"be":[30,81],"additive":[31],"with":[32,65,69],"two":[33],"possibilities:":[34],"absolute":[35],"bounded":[37],"by":[38],"a":[39,91,102],"constant,":[40],"and":[41,61,108,117],"relative":[42],"proportional":[44],"norm":[47],"gradient.":[50],"We":[51,99],"accumulation":[54],"errors":[57],"strongly":[62],"settings":[64],"main":[67],"difference":[68],"most":[70],"previous":[73],"works":[74],"being":[75],"that":[76],"feasible":[78],"set":[79],"can":[80],"unbounded.":[82],"key":[84],"latter":[87],"prove":[90],"bound":[92],"trajectory":[95],"algorithm.":[98],"also":[100],"give":[101],"stopping":[103],"criterion":[104],"algorithm":[107],"consider":[109],"extensions":[110],"cases":[113],"stochastic":[115],"composite":[118],"nonsmooth":[119],"problems.":[120]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-26T13:28:51.108037","created_date":"2025-10-10T00:00:00"}