{"id":"https://openalex.org/W2964030914","doi":"https://doi.org/10.1109/cdc.2010.5717836","title":"Convergence and convergence rate of stochastic gradient search in the case of multiple and non-isolated extrema","display_name":"Convergence and convergence rate of stochastic gradient search in the case of multiple and non-isolated extrema","publication_year":2010,"publication_date":"2010-12-01","ids":{"openalex":"https://openalex.org/W2964030914","doi":"https://doi.org/10.1109/cdc.2010.5717836","mag":"2964030914"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2010.5717836","pdf_url":null,"source":{"id":"https://openalex.org/S4363607724","display_name":"2021 60th IEEE Conference on Decision and Control (CDC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"proceedings-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://arxiv.org/pdf/0907.1020","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075157489","display_name":"Vladislav B. Tadi\u0107","orcid":"https://orcid.org/0000-0001-5805-9265"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"funder","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Vladislav B. Tadic","raw_affiliation_strings":["Department of Mathematics, University of Bristol, Bristol, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Bristol, Bristol, United Kingdom","institution_ids":["https://openalex.org/I36234482"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5075157489"],"corresponding_institution_ids":["https://openalex.org/I36234482"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":3,"citation_normalized_percentile":{"value":0.668639,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":75,"max":77},"biblio":{"volume":null,"issue":null,"first_page":"5321","last_page":"5326"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9954,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10136","display_name":"Statistical Methods and Inference","score":0.9954,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11236","display_name":"Control Systems and Identification","score":0.9835,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9823,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/hessian-matrix","display_name":"Hessian matrix","score":0.82365555},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.81789017},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic Gradient Descent","score":0.47860807}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.82365555},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.81789017},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6595758},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6389371},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.62712955},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5664357},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.54602337},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.47860807},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.43259728},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38323164},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23878208},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19919965},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.16395172},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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}],"mesh":[],"locations_count":3,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2010.5717836","pdf_url":null,"source":{"id":"https://openalex.org/S4363607724","display_name":"2021 60th IEEE Conference on Decision and Control (CDC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0907.1020","pdf_url":"http://arxiv.org/pdf/0907.1020","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/0907.1020","pdf_url":"https://arxiv.org/pdf/0907.1020","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0907.1020","pdf_url":"http://arxiv.org/pdf/0907.1020","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.56}],"grants":[],"datasets":[],"versions":[],"referenced_works_count":39,"referenced_works":["https://openalex.org/W1499021337","https://openalex.org/W1501203061","https://openalex.org/W1509448450","https://openalex.org/W1509685104","https://openalex.org/W1540723801","https://openalex.org/W1554944419","https://openalex.org/W1557899381","https://openalex.org/W1568229137","https://openalex.org/W1568288633","https://openalex.org/W1568668329","https://openalex.org/W178056938","https://openalex.org/W1826269386","https://openalex.org/W1965324089","https://openalex.org/W1971942712","https://openalex.org/W1974006687","https://openalex.org/W2007854530","https://openalex.org/W2009303086","https://openalex.org/W2021361347","https://openalex.org/W2022541060","https://openalex.org/W203276351","https://openalex.org/W2049631384","https://openalex.org/W2063685783","https://openalex.org/W2071983464","https://openalex.org/W2077612096","https://openalex.org/W2084687242","https://openalex.org/W2094358762","https://openalex.org/W2095962350","https://openalex.org/W2120339885","https://openalex.org/W2124776405","https://openalex.org/W2133515443","https://openalex.org/W2145677862","https://openalex.org/W2156291705","https://openalex.org/W2171033594","https://openalex.org/W222645141","https://openalex.org/W2331639718","https://openalex.org/W2487144912","https://openalex.org/W271314235","https://openalex.org/W4254313632","https://openalex.org/W4307347247"],"related_works":["https://openalex.org/W4221162014","https://openalex.org/W3177326532","https://openalex.org/W3143650729","https://openalex.org/W3118431319","https://openalex.org/W3004700632","https://openalex.org/W2466106906","https://openalex.org/W2355987247","https://openalex.org/W2169345436","https://openalex.org/W2153649672","https://openalex.org/W2115886818"],"abstract_inverted_index":{"The":[0],"asymptotic":[1,48,86],"behavior":[2,87],"of":[3,13,44,73,88],"stochastic":[4,61],"gradient":[5,17,62],"algorithms":[6],"is":[7,23,77,94],"studied.":[8],"Relying":[9],"on":[10,31],"some":[11],"results":[12,49],"differential":[14],"geometry":[15],"(Lojasiewicz":[16],"inequality),":[18],"the":[19,32,47,55,60,71,74,82,85],"almost":[20,28],"sure":[21,29],"point-convergence":[22],"demonstrated":[24],"and":[25],"relatively":[26],"tight":[27],"bounds":[30],"convergence":[33],"rate":[34],"are":[35],"derived.":[36],"In":[37],"sharp":[38],"contrast":[39],"to":[40,64],"all":[41],"existing":[42],"result":[43],"this":[45],"kind,":[46],"obtained":[50,83],"here":[51],"do":[52],"not":[53],"require":[54],"objective":[56,75],"function":[57,76],"(associated":[58],"with":[59],"search)":[63],"have":[65],"an":[66],"isolated":[67],"minimum":[68],"at":[69],"which":[70],"Hessian":[72],"strictly":[78],"positive":[79],"definite.":[80],"Using":[81],"results,":[84],"recursive":[89],"prediction":[90],"error":[91],"identification":[92],"methods":[93],"analyzed.":[95]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2964030914","counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-03-23T13:14:35.894895","created_date":"2019-07-30"}