{"id":"https://openalex.org/W2055467852","doi":"https://doi.org/10.1137/s0363012998338806","title":"A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings","display_name":"A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2055467852","doi":"https://doi.org/10.1137/s0363012998338806","mag":"2055467852"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012998338806","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012998338806","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and 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/A5110258450","display_name":"Paul Tseng","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Paul Tseng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110258450"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":23.0186,"has_fulltext":false,"cited_by_count":1220,"citation_normalized_percentile":{"value":0.99763942,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"38","issue":"2","first_page":"431","last_page":"446"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9966999888420105,"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":0.9623000025749207,"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/mathematics","display_name":"Mathematics","score":0.8939021229743958},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.8858276605606079},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.7625718712806702},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.7582327127456665},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.5636817216873169},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5622351765632629},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5613319873809814},{"id":"https://openalex.org/keywords/strongly-monotone","display_name":"Strongly monotone","score":0.519369900226593},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.506074845790863},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4738365113735199},{"id":"https://openalex.org/keywords/projection-method","display_name":"Projection method","score":0.46261435747146606},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4496850371360779},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34198951721191406},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3398963212966919},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32083773612976074},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2697463929653168},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19281691312789917},{"id":"https://openalex.org/keywords/dykstras-projection-algorithm","display_name":"Dykstra's projection algorithm","score":0.15082895755767822}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8939021229743958},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.8858276605606079},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.7625718712806702},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7582327127456665},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5636817216873169},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5622351765632629},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5613319873809814},{"id":"https://openalex.org/C12715386","wikidata":"https://www.wikidata.org/wiki/Q7624691","display_name":"Strongly monotone","level":3,"score":0.519369900226593},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.506074845790863},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4738365113735199},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.46261435747146606},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4496850371360779},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34198951721191406},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3398963212966919},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32083773612976074},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2697463929653168},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19281691312789917},{"id":"https://openalex.org/C202426404","wikidata":"https://www.wikidata.org/wiki/Q5318686","display_name":"Dykstra's projection algorithm","level":2,"score":0.15082895755767822},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0363012998338806","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012998338806","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.42.3125","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.3125","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.math.washington.edu/pub/tseng/papers/modfb.ps.Z","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5799999833106995}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W22790054","https://openalex.org/W87821892","https://openalex.org/W94428394","https://openalex.org/W111414977","https://openalex.org/W257907672","https://openalex.org/W575273132","https://openalex.org/W763096230","https://openalex.org/W1492700492","https://openalex.org/W1519983908","https://openalex.org/W1524324710","https://openalex.org/W1557202648","https://openalex.org/W1583089965","https://openalex.org/W1669104078","https://openalex.org/W1969073096","https://openalex.org/W1970986119","https://openalex.org/W1986364567","https://openalex.org/W1987064381","https://openalex.org/W1987290518","https://openalex.org/W1987407109","https://openalex.org/W1988480861","https://openalex.org/W1998576973","https://openalex.org/W1999219269","https://openalex.org/W1999301370","https://openalex.org/W2019569173","https://openalex.org/W2033736734","https://openalex.org/W2038497950","https://openalex.org/W2042261731","https://openalex.org/W2049966847","https://openalex.org/W2053769623","https://openalex.org/W2058532290","https://openalex.org/W2061750102","https://openalex.org/W2067272684","https://openalex.org/W2075226379","https://openalex.org/W2079261074","https://openalex.org/W2080844831","https://openalex.org/W2084874367","https://openalex.org/W2087589430","https://openalex.org/W2093417350","https://openalex.org/W2099679613","https://openalex.org/W2126051190","https://openalex.org/W2132677982","https://openalex.org/W2135168902","https://openalex.org/W2135779729","https://openalex.org/W2138216979","https://openalex.org/W2143552821","https://openalex.org/W2394608080","https://openalex.org/W2582171088","https://openalex.org/W2765234090","https://openalex.org/W3149098778","https://openalex.org/W4285719527","https://openalex.org/W4299815621","https://openalex.org/W4301283118"],"related_works":["https://openalex.org/W2383497899","https://openalex.org/W2011614914","https://openalex.org/W4300843901","https://openalex.org/W1561249172","https://openalex.org/W2951312832","https://openalex.org/W2794072299","https://openalex.org/W2094957806","https://openalex.org/W1899716740","https://openalex.org/W2085771669","https://openalex.org/W4221091651"],"abstract_inverted_index":{"We":[0,34],"consider":[1],"the":[2,11,25,28,42,45,54,59,89],"forward-backward":[3],"splitting":[4],"method":[5,19,47,55,91],"for":[6,48],"finding":[7],"a":[8,36,81],"zero":[9],"of":[10,13,27,44,70,88],"sum":[12],"two":[14],"maximal":[15],"monotone":[16,49,98],"mappings.":[17],"This":[18],"is":[20,31,62],"known":[21],"to":[22,38,92],"converge":[23],"when":[24],"inverse":[26],"forward":[29,60,78],"mapping":[30,61],"strongly":[32],"monotone.":[33],"propose":[35],"modification":[37,74],"this":[39],"method,":[40],"in":[41,94],"spirit":[43],"extragradient":[46],"variational":[50,99],"inequalities,":[51],"under":[52],"which":[53],"converges":[56],"assuming":[57],"only":[58],"(Lipschitz)":[63],"continuous":[64],"on":[65],"some":[66],"closed":[67],"convex":[68,95],"subset":[69],"its":[71],"domain.":[72],"The":[73],"entails":[75],"an":[76],"additional":[77],"step":[79,83],"and":[80,97],"projection":[82],"at":[84],"each":[85],"iteration.":[86],"Applications":[87],"modified":[90],"decomposition":[93],"programming":[96],"inequalities":[100],"are":[101],"discussed.":[102]},"counts_by_year":[{"year":2026,"cited_by_count":56},{"year":2025,"cited_by_count":145},{"year":2024,"cited_by_count":129},{"year":2023,"cited_by_count":101},{"year":2022,"cited_by_count":105},{"year":2021,"cited_by_count":144},{"year":2020,"cited_by_count":91},{"year":2019,"cited_by_count":69},{"year":2018,"cited_by_count":66},{"year":2017,"cited_by_count":38},{"year":2016,"cited_by_count":32},{"year":2015,"cited_by_count":36},{"year":2014,"cited_by_count":40},{"year":2013,"cited_by_count":26},{"year":2012,"cited_by_count":15}],"updated_date":"2026-06-13T07:54:00.901334","created_date":"2025-10-10T00:00:00"}