{"id":"https://openalex.org/W4285083846","doi":"https://doi.org/10.1137/20m1360748","title":"Bregman Proximal Point Algorithm Revisited: A New Inexact Version and Its Inertial Variant","display_name":"Bregman Proximal Point Algorithm Revisited: A New Inexact Version and Its Inertial Variant","publication_year":2022,"publication_date":"2022-07-13","ids":{"openalex":"https://openalex.org/W4285083846","doi":"https://doi.org/10.1137/20m1360748"},"language":"en","primary_location":{"id":"doi:10.1137/20m1360748","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1360748","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023071921","display_name":"Lei Yang","orcid":"https://orcid.org/0000-0001-9979-8371"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lei Yang","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-9979-8371","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5064083862","display_name":"Kim-Chuan Toh","orcid":"https://orcid.org/0000-0001-7204-8933"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kim-Chuan Toh","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-7204-8933","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023071921"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2627,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.89473876,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"32","issue":"3","first_page":"1523","last_page":"1554"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.994700014591217,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.994700014591217,"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":0.9825000166893005,"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"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9747999906539917,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.6954749822616577},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5817785859107971},{"id":"https://openalex.org/keywords/bregman-divergence","display_name":"Bregman divergence","score":0.5070481300354004},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5038313269615173},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4854622483253479},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.459847092628479},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4512065351009369},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4299297332763672},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.41738349199295044},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40896353125572205},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3296806216239929},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2840026021003723},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1380983591079712}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6954749822616577},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5817785859107971},{"id":"https://openalex.org/C149073432","wikidata":"https://www.wikidata.org/wiki/Q4960382","display_name":"Bregman divergence","level":2,"score":0.5070481300354004},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5038313269615173},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4854622483253479},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.459847092628479},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4512065351009369},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4299297332763672},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.41738349199295044},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40896353125572205},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3296806216239929},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2840026021003723},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1380983591079712},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1360748","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1360748","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4860096553","display_name":null,"funder_award_id":"R-146-000-336-114","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"}],"funders":[{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W16591383","https://openalex.org/W163258351","https://openalex.org/W1501476807","https://openalex.org/W1604467579","https://openalex.org/W1953936588","https://openalex.org/W1966953121","https://openalex.org/W1982011875","https://openalex.org/W1984958640","https://openalex.org/W1986891697","https://openalex.org/W2004304255","https://openalex.org/W2007909218","https://openalex.org/W2009274429","https://openalex.org/W2016939833","https://openalex.org/W2019786292","https://openalex.org/W2032690622","https://openalex.org/W2033468335","https://openalex.org/W2037679050","https://openalex.org/W2038497950","https://openalex.org/W2042860556","https://openalex.org/W2043093325","https://openalex.org/W2067272684","https://openalex.org/W2082305681","https://openalex.org/W2082535701","https://openalex.org/W2084777452","https://openalex.org/W2090376964","https://openalex.org/W2099679613","https://openalex.org/W2101868363","https://openalex.org/W2112980792","https://openalex.org/W2124125796","https://openalex.org/W2135779729","https://openalex.org/W2138216979","https://openalex.org/W2164224215","https://openalex.org/W2167732364","https://openalex.org/W2334285086","https://openalex.org/W2535496140","https://openalex.org/W2551153860","https://openalex.org/W2612850519","https://openalex.org/W2800693632","https://openalex.org/W2963967579","https://openalex.org/W3140735157","https://openalex.org/W4206471589","https://openalex.org/W4249513058","https://openalex.org/W4249667877"],"related_works":["https://openalex.org/W2790371392","https://openalex.org/W2140505738","https://openalex.org/W4200078764","https://openalex.org/W952002620","https://openalex.org/W3185235544","https://openalex.org/W2897842840","https://openalex.org/W4221160903","https://openalex.org/W2187449906","https://openalex.org/W2962818859","https://openalex.org/W2081395119"],"abstract_inverted_index":{"We":[0],"study":[1],"a":[2,42,68,200,215,233],"general":[3],"convex":[4,223],"optimization":[5],"problem,":[6,30,108],"which":[7,51],"covers":[8,76],"various":[9],"classic":[10,34],"problems":[11,22],"in":[12,24,60,97,129],"different":[13,95,269],"areas":[14],"and":[15,40,84,157,190,217,266],"particularly":[16],"includes":[17],"many":[18],"optimal":[19,105],"transport":[20,106],"related":[21],"arising":[23],"recent":[25],"years.":[26],"To":[27],"solve":[28],"this":[29],"we":[31,179],"revisit":[32],"the":[33,49,54,65,103,112,125,130,139,158,161,192,205,211,218,252,260,277,284],"Bregman":[35],"proximal":[36,114,140,212,243],"point":[37,244],"algorithm":[38,128],"(BPPA)":[39],"introduce":[41],"new":[43],"inexact":[44,62,73,79,88,242],"stopping":[45],"condition":[46,74],"for":[47,146,166,250,282],"solving":[48,251],"subproblems,":[50],"can":[52,116],"circumvent":[53],"underlying":[55],"feasibility":[56],"difficulty":[57],"often":[58],"appearing":[59],"existing":[61,78,240],"conditions":[63,80],"when":[64,210],"problem":[66,255],"has":[67],"complex":[69],"feasible":[70],"set.":[71],"Our":[72],"also":[75,164,274],"several":[77],"as":[81,239],"special":[82],"cases":[83],"hence":[85],"makes":[86],"our":[87,109,134,167,185,230,264,280],"BPPA":[89],"(iBPPA)":[90],"more":[91],"flexible":[92],"to":[93,102,142,258],"fit":[94],"scenarios":[96],"practice.":[98],"As":[99],"an":[100,148,181],"application":[101],"standard":[104,253],"(OT)":[107],"iBPPA":[110,135,168,265],"with":[111,224],"entropic":[113],"term":[115],"bypass":[117],"some":[118,170],"numerical":[119,248],"instability":[120],"issues":[121],"that":[122],"usually":[123],"plague":[124],"popular":[126],"Sinkhorn's":[127],"OT":[131,254],"community,":[132],"since":[133],"does":[136],"not":[137],"require":[138],"parameter":[141,213],"be":[143],"very":[144],"small":[145],"obtaining":[147],"accurate":[149],"approximate":[150],"solution.":[151],"The":[152,272],"iteration":[153,193],"complexity":[154,194],"of":[155,160,184,195,204,236,263,279],"$O(1/k)$":[156],"convergence":[159,261,285],"sequence":[162],"are":[163,256],"established":[165],"under":[169,268],"mild":[171],"conditions.":[172],"Moreover,":[173],"inspired":[174],"by":[175,188],"Nesterov's":[176],"acceleration":[177],"technique,":[178],"develop":[180],"inertial":[182],"variant":[183],"iBPPA,":[186],"denoted":[187],"V-iBPPA,":[189],"establish":[191],"$O(1/k^{\\lambda})$,":[196],"where":[197],"$\\lambda\\geq1$":[198],"is":[199,214,221],"quadrangle":[201],"scaling":[202],"exponent":[203],"kernel":[206,219],"function.":[207],"In":[208],"particular,":[209],"constant":[216],"function":[220],"strongly":[222],"Lipschitz":[225],"continuous":[226],"gradient":[227],"(hence":[228],"$\\lambda=2$),":[229],"V-iBPPA":[231,267,281],"achieves":[232],"faster":[234],"rate":[235],"$O(1/k^2)$":[237],"just":[238],"accelerated":[241],"algorithms.":[245],"Some":[246],"preliminary":[247],"experiments":[249,273],"conducted":[257],"show":[259],"behaviors":[262],"inexactness":[270],"settings.":[271],"empirically":[275],"verify":[276],"potential":[278],"improving":[283],"speed.":[286]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}