{"id":"https://openalex.org/W2088299544","doi":"https://doi.org/10.1137/08073041x","title":"Some Convergence Results for Howard's Algorithm","display_name":"Some Convergence Results for Howard's Algorithm","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2088299544","doi":"https://doi.org/10.1137/08073041x","mag":"2088299544"},"language":"en","primary_location":{"id":"doi:10.1137/08073041x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/08073041x","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5001917610","display_name":"Olivier Bokanowski","orcid":"https://orcid.org/0000-0001-7108-2005"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Olivier Bokanowski","raw_affiliation_strings":["boka@math.jussieu.fr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"boka@math.jussieu.fr#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029417368","display_name":"Stefania Maroso","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stefania Maroso","raw_affiliation_strings":["Stefania.Maroso@inria.fr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Stefania.Maroso@inria.fr#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008053184","display_name":"Hasnaa Zidani","orcid":"https://orcid.org/0000-0003-3583-6863"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hasnaa Zidani","raw_affiliation_strings":["Hasnaa.Zidani@ensta.fr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hasnaa.Zidani@ensta.fr#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.6823,"has_fulltext":false,"cited_by_count":134,"citation_normalized_percentile":{"value":0.97331204,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"47","issue":"4","first_page":"3001","last_page":"3026"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"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":0.9995999932289124,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994999766349792,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7704797983169556},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5548782348632812},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.4975009262561798},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4875945448875427},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.4704747796058655},{"id":"https://openalex.org/keywords/obstacle-problem","display_name":"Obstacle problem","score":0.45903444290161133},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4282418191432953},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.42605292797088623},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.1945454478263855},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1736772656440735},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.1576468050479889}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7704797983169556},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5548782348632812},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.4975009262561798},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4875945448875427},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.4704747796058655},{"id":"https://openalex.org/C132369183","wikidata":"https://www.wikidata.org/wiki/Q3406250","display_name":"Obstacle problem","level":3,"score":0.45903444290161133},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4282418191432953},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.42605292797088623},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.1945454478263855},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1736772656440735},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.1576468050479889},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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},{"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/08073041x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/08073041x","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.232.7016","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.232.7016","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.inria.fr/docs/00/17/95/49/PDF/RR-zidani.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.904.728","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.904.728","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.inria.fr/inria-00179549/document/","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Decent work and economic growth","score":0.4699999988079071,"id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W629173031","https://openalex.org/W1483801101","https://openalex.org/W1604311391","https://openalex.org/W1964377184","https://openalex.org/W1969991893","https://openalex.org/W1977135073","https://openalex.org/W1992688650","https://openalex.org/W2017019963","https://openalex.org/W2018686874","https://openalex.org/W2022088322","https://openalex.org/W2022384521","https://openalex.org/W2023142000","https://openalex.org/W2026365342","https://openalex.org/W2027438381","https://openalex.org/W2028145673","https://openalex.org/W2031520946","https://openalex.org/W2042680115","https://openalex.org/W2059417779","https://openalex.org/W2061508005","https://openalex.org/W2063318629","https://openalex.org/W2067547116","https://openalex.org/W2076424721","https://openalex.org/W2077264691","https://openalex.org/W2087003257","https://openalex.org/W2099438388","https://openalex.org/W2112729692","https://openalex.org/W2113734366","https://openalex.org/W2127061658","https://openalex.org/W2141436719","https://openalex.org/W2148936780","https://openalex.org/W2170316986","https://openalex.org/W2177195156","https://openalex.org/W2213161892","https://openalex.org/W2327148624","https://openalex.org/W2341171179","https://openalex.org/W2466450097","https://openalex.org/W4231495859"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W4380682190","https://openalex.org/W2334479858","https://openalex.org/W2799209613","https://openalex.org/W2028161456"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3],"convergence":[4,40,106],"results":[5],"of":[6,12,51,58,75,79,107,117,126,164,171,180],"Howard's":[7,52,108,135],"algorithm":[8,53,109,136,142],"for":[9,54,185],"the":[10,47,59,72,80,105,118,124,132,162,169,186],"resolution":[11],"$\\min_{a\\in\\mathcal{A}}":[13],"(B^a":[14],"x":[15],"-":[16,64,84,87],"c^a)":[17],"=":[18,66,89],"0$,":[19,90],"where":[20,91],"$B^a$":[21],"is":[22,26,31,93],"a":[23,27,32,37,43,55,100,138],"matrix,":[24],"$c^a$":[25],"vector,":[28],"and":[29,137,147,176,184],"$\\mathcal{A}$":[30],"compact":[33],"set.":[34],"We":[35],"show":[36,104],"global":[38],"superlinear":[39],"result,":[41],"under":[42],"monotonicity":[44,101],"assumption":[45],"on":[46,161],"matrices":[48],"$B^a$.":[49],"Extensions":[50],"max-min":[56],"problem":[57,78],"form":[60,81],"$\\max_{b\\in\\mathcal{B}}":[61],"\\min_{a\\in\\mathcal{A}}":[62],"(B^{a,b}x":[63],"c^{a,b})":[65],"0$":[67],"are":[68,159],"also":[69],"proposed.":[70],"In":[71],"particular":[73],"case":[74,125],"an":[76,94,127],"obstacle":[77,128],"$\\min":[82],"(Ax":[83],"b,$":[85],"$x":[86],"g)":[88],"A":[92],"$N":[95],"\\times":[96],"N$":[97],"matrix":[98],"satisfying":[99],"assumption,":[102],"we":[103,130],"in":[110,123,168],"no":[111],"more":[112],"than":[113],"N":[114],"iterations,":[115],"instead":[116],"usual":[119],"$2^N$":[120],"bound.":[121],"Still":[122],"problem,":[129],"establish":[131],"equivalence":[133],"between":[134],"primal-dual":[139],"active":[140],"set":[141],"[M.":[143],"Hinterm\u00fcller,":[144],"K.":[145,148],"Ito,":[146],"Kunisch,":[149],"SIAM":[150],"J.":[151],"Optim.,":[152],"13":[153],"(2002),":[154],"pp.":[155],"865\u2013888].":[156],"The":[157],"algorithms":[158],"illustrated":[160],"discretization":[163],"nonlinear":[165],"PDEs":[166],"arising":[167],"context":[170],"mathematical":[172],"finance":[173],"(American":[174],"option":[175],"Merton's":[177],"portfolio":[178],"problem),":[179],"front":[181],"propagation":[182],"problems,":[183],"double-obstacle":[187],"problem.":[188]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":16},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":9}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
