{"id":"https://openalex.org/W2073631555","doi":"https://doi.org/10.1137/s0036142903429730","title":"Adaptive Optimization of Convex Functionals in Banach Spaces","display_name":"Adaptive Optimization of Convex Functionals in Banach Spaces","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2073631555","doi":"https://doi.org/10.1137/s0036142903429730","mag":"2073631555"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142903429730","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903429730","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/A5007738501","display_name":"Claudio Canuto","orcid":"https://orcid.org/0000-0002-8481-0312"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Claudio Canuto","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5008601082","display_name":"Karsten Urban","orcid":"https://orcid.org/0000-0002-6262-7955"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Karsten Urban","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4416,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.88110079,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"42","issue":"5","first_page":"2043","last_page":"2075"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9995999932289124,"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":0.9995999932289124,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9983000159263611,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9975000023841858,"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":0.9001687169075012},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.7492579817771912},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5851571559906006},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5373875498771667},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5282822251319885},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5234484076499939},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5100696682929993},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.49125903844833374},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.484425812959671},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4828370213508606},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.44599440693855286},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4228634834289551},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3710084557533264},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3488166928291321}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9001687169075012},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.7492579817771912},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5851571559906006},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5373875498771667},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5282822251319885},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5234484076499939},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5100696682929993},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.49125903844833374},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.484425812959671},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4828370213508606},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.44599440693855286},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4228634834289551},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3710084557533264},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3488166928291321},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","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/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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142903429730","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903429730","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:porto.polito.it:1471662","is_oa":false,"landing_page_url":"http://porto.polito.it/1471662/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402038","display_name":"PORTO Publications Open Repository TOrino (Politecnico di Torino)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177477856","host_organization_name":"Politecnico di Torino","host_organization_lineage":["https://openalex.org/I177477856"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:0036-1429","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1532491804","https://openalex.org/W1533889494","https://openalex.org/W1537335979","https://openalex.org/W1539855477","https://openalex.org/W1549732571","https://openalex.org/W1553702074","https://openalex.org/W1653619892","https://openalex.org/W1972883869","https://openalex.org/W1980036126","https://openalex.org/W1988406495","https://openalex.org/W1993247264","https://openalex.org/W1995479616","https://openalex.org/W2004261587","https://openalex.org/W2015219711","https://openalex.org/W2039924562","https://openalex.org/W2045050233","https://openalex.org/W2048268779","https://openalex.org/W2048834141","https://openalex.org/W2059870147","https://openalex.org/W2068484625","https://openalex.org/W2079275676","https://openalex.org/W2082131680","https://openalex.org/W2084743165","https://openalex.org/W2099209065","https://openalex.org/W2107829755","https://openalex.org/W2109400831","https://openalex.org/W2115566547","https://openalex.org/W2502261143","https://openalex.org/W3091814460","https://openalex.org/W3099881437","https://openalex.org/W3118870036","https://openalex.org/W4253214256","https://openalex.org/W4296816584"],"related_works":["https://openalex.org/W1507633639","https://openalex.org/W3151522584","https://openalex.org/W4297883503","https://openalex.org/W4313177131","https://openalex.org/W4292651679","https://openalex.org/W2400034325","https://openalex.org/W2499557797","https://openalex.org/W2985014567","https://openalex.org/W4299515259","https://openalex.org/W2032676126"],"abstract_inverted_index":{"This":[0,86],"paper":[1],"is":[2,88,127],"concerned":[3],"with":[4],"optimization":[5],"or":[6,19],"minimization":[7,61],"problems":[8],"that":[9,99,123],"are":[10,24,109],"governed":[11],"by":[12],"operator":[13],"equations,":[14,21],"such":[15],"as":[16],"partial":[17],"differential":[18],"integral":[20],"and":[22,46,121],"thus":[23],"naturally":[25],"formulated":[26],"in":[27,44,55,68,84,101],"an":[28,64,81],"infinite":[29],"dimensional":[30],"function":[31],"space":[32,71],"V.":[33],"We":[34,75],"first":[35],"construct":[36],"a":[37,52,69],"prototype":[38,78],"algorithm":[39,79,87,120],"of":[40,72,116,118],"steepest":[41],"descent":[42],"type":[43,73],"V":[45,56],"prove":[47,122],"its":[48],"convergence.":[49],"By":[50],"using":[51],"Riesz":[53],"basis":[54],"we":[57,108,131],"can":[58],"transform":[59],"the":[60,77,97,102,114,124],"problem":[62],"into":[63,80],"equivalent":[65],"one":[66],"posed":[67],"sequence":[70],"$\\ell_p$.":[74,85],"convert":[76],"adaptive":[82],"method":[83],"shown":[89],"to":[90,112],"be":[91],"convergent":[92],"under":[93],"mild":[94],"conditions":[95],"on":[96],"parameters":[98],"appear":[100],"algorithm.":[103],"Under":[104],"more":[105],"restrictive":[106],"assumptions":[107],"also":[110],"able":[111],"establish":[113],"rate":[115],"convergence":[117],"our":[119],"work/accuracy":[125],"balance":[126],"asymptotically":[128],"optimal.":[129],"Finally,":[130],"give":[132],"two":[133],"particular":[134],"examples.":[135]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
