{"id":"https://openalex.org/W2018711500","doi":"https://doi.org/10.1137/03060062x","title":"Robust Stopping Criteria for Dykstra's Algorithm","display_name":"Robust Stopping Criteria for Dykstra's Algorithm","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2018711500","doi":"https://doi.org/10.1137/03060062x","mag":"2018711500"},"language":"en","primary_location":{"id":"doi:10.1137/03060062x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/03060062x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.1137/03060062X","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087290455","display_name":"Ernesto G. Birgin","orcid":"https://orcid.org/0000-0002-7466-7663"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ernesto G. Birgin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5049891878","display_name":"Marcos Raydan","orcid":"https://orcid.org/0000-0003-0417-7981"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marcos Raydan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8618,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.73221076,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"26","issue":"4","first_page":"1405","last_page":"1414"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9972000122070312,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9972000122070312,"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/T12288","display_name":"Optimization and Search Problems","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9962000250816345,"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/counterexample","display_name":"Counterexample","score":0.7373667359352112},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7324023246765137},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6907330751419067},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5918430089950562},{"id":"https://openalex.org/keywords/optimal-stopping","display_name":"Optimal stopping","score":0.576237142086029},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5400576591491699},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5180885195732117},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5115004777908325},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.44875064492225647},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18236574530601501}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.7373667359352112},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7324023246765137},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6907330751419067},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5918430089950562},{"id":"https://openalex.org/C99414536","wikidata":"https://www.wikidata.org/wiki/Q7098950","display_name":"Optimal stopping","level":2,"score":0.576237142086029},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5400576591491699},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5180885195732117},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5115004777908325},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.44875064492225647},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18236574530601501},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/03060062x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/03060062x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:001450943","is_oa":true,"landing_page_url":"https://doi.org/10.1137/03060062X","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"reponame:Reposit\u00f3rio Institucional da USP (Biblioteca Digital da Produ\u00e7\u00e3o Intelectual)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.67.3846","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.67.3846","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ime.usp.br/~egbirgin/publications/br.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:001450943","is_oa":true,"landing_page_url":"https://doi.org/10.1137/03060062X","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"reponame:Reposit\u00f3rio Institucional da USP (Biblioteca Digital da Produ\u00e7\u00e3o Intelectual)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W146716711","https://openalex.org/W1497941563","https://openalex.org/W1536329667","https://openalex.org/W1710475132","https://openalex.org/W1754998723","https://openalex.org/W1964922595","https://openalex.org/W1967340927","https://openalex.org/W1987929122","https://openalex.org/W2000389722","https://openalex.org/W2004328411","https://openalex.org/W2016425264","https://openalex.org/W2021897193","https://openalex.org/W2022393739","https://openalex.org/W2030942503","https://openalex.org/W2032516292","https://openalex.org/W2040847644","https://openalex.org/W2042863194","https://openalex.org/W2047043241","https://openalex.org/W2050958540","https://openalex.org/W2052276588","https://openalex.org/W2054821093","https://openalex.org/W2055610959","https://openalex.org/W2062694825","https://openalex.org/W2078328129","https://openalex.org/W2084263592","https://openalex.org/W2091560152","https://openalex.org/W2093637117","https://openalex.org/W2106686997","https://openalex.org/W2163392119","https://openalex.org/W2249828319","https://openalex.org/W4229812070","https://openalex.org/W4238637266"],"related_works":["https://openalex.org/W2349952486","https://openalex.org/W1489260687","https://openalex.org/W2775700832","https://openalex.org/W2587222766","https://openalex.org/W3204670144","https://openalex.org/W2163101548","https://openalex.org/W1988934358","https://openalex.org/W4389574038","https://openalex.org/W4387718369","https://openalex.org/W3153752017"],"abstract_inverted_index":{"Dykstra's":[0],"algorithm":[1],"is":[2],"a":[3,25,39,63,77],"suitable":[4],"alternating":[5],"projection":[6],"scheme":[7],"for":[8],"solving":[9],"the":[10,15,22,47,58,69,81,84,102],"optimization":[11,70],"problem":[12],"of":[13,24,28,42,83,104],"finding":[14],"closest":[16],"point":[17,64],"to":[18,79,100],"one":[19],"given":[20],"in":[21,38,45],"intersection":[23],"finite":[26],"number":[27],"closed":[29],"and":[30,55,88],"convex":[31],"sets.":[32],"It":[33],"has":[34],"been":[35],"recently":[36],"used":[37,49,86],"wide":[40],"variety":[41],"applications.":[43],"However,":[44],"practice,":[46],"commonly":[48,85],"stopping":[50,93,107],"criteria":[51],"are":[52,98],"not":[53,67],"robust":[54,92],"could":[56],"stop":[57],"iterative":[59],"process":[60],"prematurely":[61],"at":[62],"that":[65],"does":[66],"solve":[68],"problem.":[71],"In":[72],"this":[73,105],"work":[74],"we":[75,90],"present":[76],"counterexample":[78],"illustrate":[80,101],"weakness":[82],"criteria,":[87,108],"then":[89],"develop":[91],"rules.":[94],"Additional":[95],"experimental":[96],"results":[97],"shown":[99],"advantages":[103],"new":[106],"including":[109],"their":[110],"associated":[111],"computational":[112],"cost.":[113]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
