{"id":"https://openalex.org/W3166920677","doi":"https://doi.org/10.3390/a14060174","title":"An Introduction to Development of Centralized and Distributed Stochastic Approximation Algorithm with Expanding Truncations","display_name":"An Introduction to Development of Centralized and Distributed Stochastic Approximation Algorithm with Expanding Truncations","publication_year":2021,"publication_date":"2021-05-31","ids":{"openalex":"https://openalex.org/W3166920677","doi":"https://doi.org/10.3390/a14060174","mag":"3166920677"},"language":"en","primary_location":{"id":"doi:10.3390/a14060174","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a14060174","pdf_url":"https://www.mdpi.com/1999-4893/14/6/174/pdf?version=1622602748","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/14/6/174/pdf?version=1622602748","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101465051","display_name":"Wenxiao Zhao","orcid":"https://orcid.org/0000-0002-0371-5664"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wenxiao Zhao","raw_affiliation_strings":["Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China","School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China","institution_ids":["https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101465051"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485","https://openalex.org/I4210165038"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07955427,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"6","first_page":"174","last_page":"174"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9997000098228455,"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/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.994700014591217,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.7659487724304199},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6380242705345154},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.624194860458374},{"id":"https://openalex.org/keywords/development","display_name":"Development (topology)","score":0.55962735414505},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.528813362121582},{"id":"https://openalex.org/keywords/stochastic-approximation","display_name":"Stochastic approximation","score":0.5281384587287903},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.52810138463974},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.4903850555419922},{"id":"https://openalex.org/keywords/subsequence","display_name":"Subsequence","score":0.44306522607803345},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.43497195839881897},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3549257516860962},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.33405226469039917},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.29750722646713257},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.257241427898407},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.20257550477981567},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.14951938390731812}],"concepts":[{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.7659487724304199},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6380242705345154},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.624194860458374},{"id":"https://openalex.org/C2776542497","wikidata":"https://www.wikidata.org/wiki/Q5266672","display_name":"Development (topology)","level":2,"score":0.55962735414505},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.528813362121582},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.5281384587287903},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.52810138463974},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4903850555419922},{"id":"https://openalex.org/C137877099","wikidata":"https://www.wikidata.org/wiki/Q1332977","display_name":"Subsequence","level":3,"score":0.44306522607803345},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.43497195839881897},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3549257516860962},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33405226469039917},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.29750722646713257},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.257241427898407},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.20257550477981567},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.14951938390731812},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0},{"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a14060174","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a14060174","pdf_url":"https://www.mdpi.com/1999-4893/14/6/174/pdf?version=1622602748","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:1d5d5e2064a24bd2bdcd0b0d1ae9f449","is_oa":true,"landing_page_url":"https://doaj.org/article/1d5d5e2064a24bd2bdcd0b0d1ae9f449","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 14, Iss 6, p 174 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/14/6/174/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a14060174","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms; Volume 14; Issue 6; Pages: 174","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a14060174","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a14060174","pdf_url":"https://www.mdpi.com/1999-4893/14/6/174/pdf?version=1622602748","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1121271761","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3931757239","display_name":null,"funder_award_id":"2018YFA0703800","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G5848258319","display_name":null,"funder_award_id":"0 and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8073047987","display_name":null,"funder_award_id":"2018YFA0703","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G8280473804","display_name":null,"funder_award_id":"61822312","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3166920677.pdf","grobid_xml":"https://content.openalex.org/works/W3166920677.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W103934657","https://openalex.org/W197263747","https://openalex.org/W1501203061","https://openalex.org/W1965055646","https://openalex.org/W1967049706","https://openalex.org/W1974720542","https://openalex.org/W1975193898","https://openalex.org/W1975286263","https://openalex.org/W1979043738","https://openalex.org/W1979761486","https://openalex.org/W1984046189","https://openalex.org/W1984519003","https://openalex.org/W1994457938","https://openalex.org/W1994616650","https://openalex.org/W2000539579","https://openalex.org/W2010552022","https://openalex.org/W2010586736","https://openalex.org/W2044212084","https://openalex.org/W2045334340","https://openalex.org/W2047445817","https://openalex.org/W2047977296","https://openalex.org/W2054127449","https://openalex.org/W2056616149","https://openalex.org/W2080631849","https://openalex.org/W2083005466","https://openalex.org/W2092667969","https://openalex.org/W2092911205","https://openalex.org/W2099175737","https://openalex.org/W2107396783","https://openalex.org/W2108641449","https://openalex.org/W2114791779","https://openalex.org/W2118776392","https://openalex.org/W2122569148","https://openalex.org/W2130059151","https://openalex.org/W2148401037","https://openalex.org/W2170629618","https://openalex.org/W2235056388","https://openalex.org/W2273484141","https://openalex.org/W2440591613","https://openalex.org/W2531891978","https://openalex.org/W2556047458","https://openalex.org/W2767699304","https://openalex.org/W2808584793","https://openalex.org/W2964337808","https://openalex.org/W3141362395","https://openalex.org/W4302033506","https://openalex.org/W6996586349","https://openalex.org/W7006019768"],"related_works":["https://openalex.org/W3082668976","https://openalex.org/W2517973022","https://openalex.org/W1543121148","https://openalex.org/W1580703421","https://openalex.org/W2618518959","https://openalex.org/W2231364979","https://openalex.org/W4295745414","https://openalex.org/W4382202915","https://openalex.org/W4288093367","https://openalex.org/W2489516236"],"abstract_inverted_index":{"The":[0],"stochastic":[1,46],"approximation":[2,47],"algorithm":[3,48,74],"(SAA),":[4],"starting":[5],"from":[6],"the":[7,36,45,61,68,72,76,81,90,105,114,126],"pioneer":[8],"work":[9],"by":[10,54],"Robbins":[11],"and":[12,22,27,57,80,89,122],"Monro":[13],"in":[14,20,40,119],"1950s,":[15],"has":[16],"been":[17],"successfully":[18],"applied":[19],"systems":[21],"control,":[23],"statistics,":[24],"machine":[25],"learning,":[26],"so":[28],"forth.":[29],"In":[30],"this":[31],"paper,":[32],"we":[33,96],"will":[34,97,111],"review":[35,67],"development":[37,70],"of":[38,102],"SAA":[39,88],"China,":[41],"to":[42,104],"be":[43],"specific,":[44],"with":[49],"expanding":[50],"truncations":[51],"(SAAWET)":[52],"developed":[53],"Han-Fu":[55],"Chen":[56],"his":[58],"colleagues":[59],"during":[60],"past":[62],"35":[63],"years.":[64],"We":[65,110],"first":[66],"historical":[69],"for":[71,87,93],"centralized":[73],"including":[75],"probabilistic":[77],"method":[78,86,92],"(PM)":[79],"ordinary":[82],"differential":[83],"equation":[84],"(ODE)":[85],"trajectory-subsequence":[91],"SAAWET.":[94],"Then,":[95],"give":[98],"an":[99],"application":[100],"example":[101],"SAAWET":[103,118,128],"recursive":[106],"principal":[107],"component":[108],"analysis.":[109],"also":[112],"introduce":[113],"recent":[115],"progress":[116],"on":[117],"a":[120],"networked":[121],"distributed":[123,127],"setting,":[124],"named":[125],"(DSAAWET).":[129]},"counts_by_year":[],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}