{"id":"https://openalex.org/W3027891624","doi":"https://doi.org/10.1137/18m1207260","title":"A Forward-Backward Splitting Method for Monotone Inclusions Without Cocoercivity","display_name":"A Forward-Backward Splitting Method for Monotone Inclusions Without Cocoercivity","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3027891624","doi":"https://doi.org/10.1137/18m1207260","mag":"3027891624"},"language":"en","primary_location":{"id":"doi:10.1137/18m1207260","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1207260","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":"https://resolver.sub.uni-goettingen.de/purl?gro-2/136140","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108689235","display_name":"Yura Malitsky","orcid":null},"institutions":[{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Yura Malitsky","raw_affiliation_strings":["Institute for Numerical and Applied Mathematics, University of G\u00f6ttingen, 37083 G\u00f6ttingen, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Numerical and Applied Mathematics, University of G\u00f6ttingen, 37083 G\u00f6ttingen, Germany","institution_ids":["https://openalex.org/I74656192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029600817","display_name":"Matthew K. Tam","orcid":"https://orcid.org/0000-0002-3654-6553"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"The University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]},{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["AU","DE"],"is_corresponding":false,"raw_author_name":"Matthew K. Tam","raw_affiliation_strings":["School of Mathematics & Statistics, The University of Melbourne, Parkville VIC 3010, Australia","Institute for Numerical and Applied Mathematics, University of G\u00f6ttingen, 37083 G\u00f6ttingen, Germany"],"affiliations":[{"raw_affiliation_string":"School of Mathematics & Statistics, The University of Melbourne, Parkville VIC 3010, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Institute for Numerical and Applied Mathematics, University of G\u00f6ttingen, 37083 G\u00f6ttingen, Germany","institution_ids":["https://openalex.org/I74656192"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5108689235"],"corresponding_institution_ids":["https://openalex.org/I74656192"],"apc_list":null,"apc_paid":null,"fwci":45.3732,"has_fulltext":false,"cited_by_count":228,"citation_normalized_percentile":{"value":0.99972467,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"30","issue":"2","first_page":"1451","last_page":"1472"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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":0.9984999895095825,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9976999759674072,"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":0.8716858625411987},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.8068826198577881},{"id":"https://openalex.org/keywords/operator-splitting","display_name":"Operator splitting","score":0.7729198932647705},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5999775528907776},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5351638793945312},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4958086907863617},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.4896264672279358},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.44424453377723694},{"id":"https://openalex.org/keywords/inertia","display_name":"Inertia","score":0.4432116150856018},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3527122139930725},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23303836584091187},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.053906381130218506}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8716858625411987},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.8068826198577881},{"id":"https://openalex.org/C2987355758","wikidata":"https://www.wikidata.org/wiki/Q25037251","display_name":"Operator splitting","level":2,"score":0.7729198932647705},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5999775528907776},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5351638793945312},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4958086907863617},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.4896264672279358},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.44424453377723694},{"id":"https://openalex.org/C110407247","wikidata":"https://www.wikidata.org/wiki/Q122508","display_name":"Inertia","level":2,"score":0.4432116150856018},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3527122139930725},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23303836584091187},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.053906381130218506},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/18m1207260","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1207260","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:publications.goettingen-research-online.de:2/136140","is_oa":true,"landing_page_url":"https://resolver.sub.uni-goettingen.de/purl?gro-2/136140","pdf_url":null,"source":{"id":"https://openalex.org/S4306401634","display_name":"GoeScholar  The Publication Server of the Georg-August-Universit\u00e4t G\u00f6ttingen (Georg-August-Universit\u00e4t G\u00f6ttingen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210122495","host_organization_name":"Asklepios Klinik St. Georg","host_organization_lineage":["https://openalex.org/I4210122495"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:publications.goettingen-research-online.de:2/82285","is_oa":true,"landing_page_url":"https://resolver.sub.uni-goettingen.de/purl?gro-2/82285","pdf_url":null,"source":{"id":"https://openalex.org/S4306401634","display_name":"GoeScholar  The Publication Server of the Georg-August-Universit\u00e4t G\u00f6ttingen (Georg-August-Universit\u00e4t G\u00f6ttingen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210122495","host_organization_name":"Asklepios Klinik St. Georg","host_organization_lineage":["https://openalex.org/I4210122495"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:publications.goettingen-research-online.de:2/136140","is_oa":true,"landing_page_url":"https://resolver.sub.uni-goettingen.de/purl?gro-2/136140","pdf_url":null,"source":{"id":"https://openalex.org/S4306401634","display_name":"GoeScholar  The Publication Server of the Georg-August-Universit\u00e4t G\u00f6ttingen (Georg-August-Universit\u00e4t G\u00f6ttingen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210122495","host_organization_name":"Asklepios Klinik St. Georg","host_organization_lineage":["https://openalex.org/I4210122495"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"score":0.5400000214576721,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G3307378536","display_name":null,"funder_award_id":"Fellow","funder_id":"https://openalex.org/F4320308269","funder_display_name":"Alexander von Humboldt-Stiftung"},{"id":"https://openalex.org/G5418744004","display_name":null,"funder_award_id":"SFB755","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8526424774","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G963958558","display_name":null,"funder_award_id":"SFB755-A4","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W199410564","https://openalex.org/W1493782845","https://openalex.org/W1560858410","https://openalex.org/W1967317714","https://openalex.org/W1981558178","https://openalex.org/W1989464734","https://openalex.org/W1991386640","https://openalex.org/W2019569173","https://openalex.org/W2030161963","https://openalex.org/W2038497950","https://openalex.org/W2055467852","https://openalex.org/W2056578325","https://openalex.org/W2080844831","https://openalex.org/W2081985785","https://openalex.org/W2092663520","https://openalex.org/W2095980290","https://openalex.org/W2559655401","https://openalex.org/W2795507584","https://openalex.org/W2921509219","https://openalex.org/W2950866122","https://openalex.org/W2963654173","https://openalex.org/W2989034963","https://openalex.org/W3021478246","https://openalex.org/W3099827691","https://openalex.org/W3101497372","https://openalex.org/W3123649567"],"related_works":["https://openalex.org/W1489292980","https://openalex.org/W2951610245","https://openalex.org/W2795079910","https://openalex.org/W1430963189","https://openalex.org/W1974262772","https://openalex.org/W2049901819","https://openalex.org/W3037410748","https://openalex.org/W2052430123","https://openalex.org/W1983437306","https://openalex.org/W4387778523"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3],"propose":[4],"a":[5,15,68,74],"simple":[6],"modification":[7],"of":[8,20,41,64],"the":[9,18,28,42,58,65],"forward-backward":[10],"splitting":[11],"method":[12,25,66],"for":[13,60],"finding":[14],"zero":[16],"in":[17],"sum":[19],"two":[21,55],"monotone":[22],"operators.":[23],"Our":[24],"converges":[26],"under":[27],"same":[29],"assumptions":[30],"as":[31,56],"Tseng's":[32,61],"forward-backward-forward":[33],"method,":[34],"namely,":[35],"it":[36],"does":[37],"not":[38],"require":[39],"cocoercivity":[40],"single-valued":[43],"operator.":[44],"Moreover,":[45],"each":[46],"iteration":[47],"only":[48],"uses":[49],"one":[50],"forward":[51],"evaluation":[52],"rather":[53],"than":[54],"is":[57],"case":[59],"method.":[62],"Variants":[63],"incorporating":[67],"linesearch,":[69],"relaxation":[70],"and":[71],"inertia,":[72],"or":[73],"structured":[75],"three":[76],"operator":[77],"inclusion":[78],"are":[79],"also":[80],"discussed.":[81]},"counts_by_year":[{"year":2026,"cited_by_count":17},{"year":2025,"cited_by_count":42},{"year":2024,"cited_by_count":49},{"year":2023,"cited_by_count":45},{"year":2022,"cited_by_count":33},{"year":2021,"cited_by_count":27},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":4}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
