{"id":"https://openalex.org/W4310154446","doi":"https://doi.org/10.1007/s10957-022-02125-9","title":"Bregman Three-Operator Splitting Methods","display_name":"Bregman Three-Operator Splitting Methods","publication_year":2022,"publication_date":"2022-11-28","ids":{"openalex":"https://openalex.org/W4310154446","doi":"https://doi.org/10.1007/s10957-022-02125-9"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-022-02125-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-022-02125-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-022-02125-9.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10957-022-02125-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091239383","display_name":"Xin Jiang","orcid":"https://orcid.org/0000-0003-1231-8529"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Xin Jiang","raw_affiliation_strings":["University of California, Los Angeles, Los Angeles, CA, 90095, USA"],"affiliations":[{"raw_affiliation_string":"University of California, Los Angeles, Los Angeles, CA, 90095, USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017990990","display_name":"Lieven Vandenberghe","orcid":"https://orcid.org/0000-0003-4153-2268"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lieven Vandenberghe","raw_affiliation_strings":["University of California, Los Angeles, Los Angeles, CA, 90095, USA"],"affiliations":[{"raw_affiliation_string":"University of California, Los Angeles, Los Angeles, CA, 90095, USA","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5091239383"],"corresponding_institution_ids":["https://openalex.org/I161318765"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.3577,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.83396377,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"196","issue":"3","first_page":"936","last_page":"972"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9979000091552734,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9921000003814697,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bregman-divergence","display_name":"Bregman divergence","score":0.7671222686767578},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7353078126907349},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6972249150276184},{"id":"https://openalex.org/keywords/operator-splitting","display_name":"Operator splitting","score":0.5975030660629272},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5634945631027222},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5596569180488586},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5435410141944885},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5065680742263794},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4925842881202698},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4768146872520447},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.46828290820121765},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42537909746170044},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.41533392667770386},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.2974775433540344},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19811975955963135}],"concepts":[{"id":"https://openalex.org/C149073432","wikidata":"https://www.wikidata.org/wiki/Q4960382","display_name":"Bregman divergence","level":2,"score":0.7671222686767578},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7353078126907349},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6972249150276184},{"id":"https://openalex.org/C2987355758","wikidata":"https://www.wikidata.org/wiki/Q25037251","display_name":"Operator splitting","level":2,"score":0.5975030660629272},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5634945631027222},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5596569180488586},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5435410141944885},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5065680742263794},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4925842881202698},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4768146872520447},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46828290820121765},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42537909746170044},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.41533392667770386},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2974775433540344},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19811975955963135},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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},{"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"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/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-022-02125-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-022-02125-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-022-02125-9.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:joptap:v:196:y:2023:i:3:d:10.1007_s10957-022-02125-9","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-022-02125-9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"}],"best_oa_location":{"id":"doi:10.1007/s10957-022-02125-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-022-02125-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-022-02125-9.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7900000214576721,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4310154446.pdf","grobid_xml":"https://content.openalex.org/works/W4310154446.grobid-xml"},"referenced_works_count":49,"referenced_works":["https://openalex.org/W158841883","https://openalex.org/W562372631","https://openalex.org/W1922442141","https://openalex.org/W1946620893","https://openalex.org/W1953936588","https://openalex.org/W1981112674","https://openalex.org/W1986891697","https://openalex.org/W1998991750","https://openalex.org/W2019569173","https://openalex.org/W2021548137","https://openalex.org/W2051882509","https://openalex.org/W2055467852","https://openalex.org/W2058532290","https://openalex.org/W2071236014","https://openalex.org/W2090376964","https://openalex.org/W2092663520","https://openalex.org/W2107941784","https://openalex.org/W2112980792","https://openalex.org/W2114423093","https://openalex.org/W2142280715","https://openalex.org/W2158449358","https://openalex.org/W2164224215","https://openalex.org/W2241435520","https://openalex.org/W2405803404","https://openalex.org/W2510358906","https://openalex.org/W2535496140","https://openalex.org/W2544610656","https://openalex.org/W2551153860","https://openalex.org/W2763081248","https://openalex.org/W2800693632","https://openalex.org/W2886903283","https://openalex.org/W2886952723","https://openalex.org/W2901838001","https://openalex.org/W2963367966","https://openalex.org/W2963496223","https://openalex.org/W2963967579","https://openalex.org/W3044707062","https://openalex.org/W3100820186","https://openalex.org/W3105279496","https://openalex.org/W3118876559","https://openalex.org/W3161273445","https://openalex.org/W3195321777","https://openalex.org/W4200490012","https://openalex.org/W4206742934","https://openalex.org/W4243792189","https://openalex.org/W4249667877","https://openalex.org/W4285085550","https://openalex.org/W4290828441","https://openalex.org/W6601216650"],"related_works":["https://openalex.org/W2883143458","https://openalex.org/W3048061938","https://openalex.org/W3202139669","https://openalex.org/W2016611950","https://openalex.org/W4280509037","https://openalex.org/W4288262114","https://openalex.org/W1986956864","https://openalex.org/W3206101938","https://openalex.org/W4226373092","https://openalex.org/W3213628111"],"abstract_inverted_index":{"Abstract":[0],"The":[1,27,42],"paper":[2],"presents":[3],"primal\u2013dual":[4,38],"proximal":[5,24,54],"splitting":[6],"methods":[7,28,77],"for":[8,70,87],"convex":[9],"optimization,":[10],"in":[11,90],"which":[12],"generalized":[13],"Bregman":[14,43,53,92,104],"distances":[15],"are":[16,49],"used":[17],"to":[18,58,97],"define":[19],"the":[20,30,37,46,52,71,75,91],"primal":[21,31],"and":[22,32,36,108],"dual":[23,33,93],"update":[25],"steps.":[26],"extend":[29],"Condat\u2013V\u0169":[34,47,94],"algorithms":[35,48],"three-operator":[39],"(PD3O)":[40],"algorithm.":[41],"extensions":[44],"of":[45,74,106],"derived":[50],"from":[51],"point":[55],"method":[56],"applied":[57,96],"a":[59,67,83,103],"monotone":[60],"inclusion":[61],"problem.":[62],"Based":[63],"on":[64],"this":[65],"interpretation,":[66],"unified":[68],"framework":[69],"convergence":[72],"analysis":[73],"two":[76],"is":[78],"presented.":[79],"We":[80],"also":[81],"introduce":[82],"line":[84],"search":[85],"procedure":[86],"stepsize":[88],"selection":[89],"algorithm":[95],"equality-constrained":[98],"problems.":[99],"Finally,":[100],"we":[101],"propose":[102],"extension":[105],"PD3O":[107],"analyze":[109],"its":[110],"convergence.":[111]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}