{"id":"https://openalex.org/W3008548982","doi":"https://doi.org/10.1109/bigdata47090.2019.9005621","title":"On the Global Convergence of Continuous\u2013Time Stochastic Heavy\u2013Ball Method for Nonconvex Optimization","display_name":"On the Global Convergence of Continuous\u2013Time Stochastic Heavy\u2013Ball Method for Nonconvex Optimization","publication_year":2019,"publication_date":"2019-12-01","ids":{"openalex":"https://openalex.org/W3008548982","doi":"https://doi.org/10.1109/bigdata47090.2019.9005621","mag":"3008548982"},"language":"en","primary_location":{"id":"doi:10.1109/bigdata47090.2019.9005621","is_oa":false,"landing_page_url":"https://doi.org/10.1109/bigdata47090.2019.9005621","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Conference on Big Data (Big Data)","raw_type":"proceedings-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/A5082454668","display_name":"Wenqing Hu","orcid":"https://orcid.org/0000-0002-6116-9104"},"institutions":[{"id":"https://openalex.org/I20382870","display_name":"Missouri University of Science and Technology","ror":"https://ror.org/00scwqd12","country_code":"US","type":"education","lineage":["https://openalex.org/I20382870"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Wenqing Hu","raw_affiliation_strings":["Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, USA","institution_ids":["https://openalex.org/I20382870"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058611209","display_name":"Chris Junchi Li","orcid":"https://orcid.org/0000-0003-0158-1655"},"institutions":[{"id":"https://openalex.org/I2250653659","display_name":"Tencent (China)","ror":"https://ror.org/00hhjss72","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250653659"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chris Junchi Li","raw_affiliation_strings":["Tencent AI Lab Tecent Technology, Shenzhen, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tencent AI Lab Tecent Technology, Shenzhen, China","institution_ids":["https://openalex.org/I2250653659"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030761097","display_name":"Xiang Zhou","orcid":"https://orcid.org/0000-0002-3835-3894"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Xiang Zhou","raw_affiliation_strings":["School of Data Science, City University of Hong Kong, Hong Kong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Data Science, City University of Hong Kong, Hong Kong, China","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5082454668"],"corresponding_institution_ids":["https://openalex.org/I20382870"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.2006835,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"94","last_page":"104"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9983000159263611,"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"}},"topics":[{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9983000159263611,"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"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9857000112533569,"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/T11996","display_name":"Random lasers and scattering media","score":0.9611999988555908,"subfield":{"id":"https://openalex.org/subfields/3102","display_name":"Acoustics and Ultrasonics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6133240461349487},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.5944947004318237},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5350222587585449},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.5258793830871582},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5157608985900879},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5107553005218506},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.5102348327636719},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5020265579223633},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.4955962896347046},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.4666103720664978},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4304875135421753},{"id":"https://openalex.org/keywords/square-root","display_name":"Square root","score":0.4105672538280487},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35495370626449585},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33690521121025085},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13083100318908691},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0892305076122284}],"concepts":[{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6133240461349487},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.5944947004318237},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5350222587585449},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.5258793830871582},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5157608985900879},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5107553005218506},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.5102348327636719},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5020265579223633},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.4955962896347046},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.4666103720664978},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4304875135421753},{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.4105672538280487},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35495370626449585},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33690521121025085},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13083100318908691},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0892305076122284},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/bigdata47090.2019.9005621","is_oa":false,"landing_page_url":"https://doi.org/10.1109/bigdata47090.2019.9005621","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Conference on Big Data (Big Data)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W104184427","https://openalex.org/W594357522","https://openalex.org/W1499021337","https://openalex.org/W1568229137","https://openalex.org/W1978065031","https://openalex.org/W1987647825","https://openalex.org/W1988720110","https://openalex.org/W1999637900","https://openalex.org/W2018394408","https://openalex.org/W2021611402","https://openalex.org/W2058385719","https://openalex.org/W2077571404","https://openalex.org/W2081817659","https://openalex.org/W2128949314","https://openalex.org/W2134618502","https://openalex.org/W2159165381","https://openalex.org/W2474090883","https://openalex.org/W2528062157","https://openalex.org/W2592651140","https://openalex.org/W2621920791","https://openalex.org/W2773083059","https://openalex.org/W2790867397","https://openalex.org/W2796146910","https://openalex.org/W2808253190","https://openalex.org/W2883160730","https://openalex.org/W2898866127","https://openalex.org/W2962781506","https://openalex.org/W2962798807","https://openalex.org/W2963092340","https://openalex.org/W2963487351","https://openalex.org/W2964072432","https://openalex.org/W2964106499","https://openalex.org/W2964265968","https://openalex.org/W3147034027","https://openalex.org/W4212958445","https://openalex.org/W4243772471","https://openalex.org/W4249520102","https://openalex.org/W4255503322","https://openalex.org/W6604254268","https://openalex.org/W6680025182","https://openalex.org/W6720643467","https://openalex.org/W6734280532","https://openalex.org/W6739826692","https://openalex.org/W6746152743","https://openalex.org/W6749200166","https://openalex.org/W6756528052"],"related_works":["https://openalex.org/W3094031457","https://openalex.org/W2767153625","https://openalex.org/W3173102712","https://openalex.org/W2389267936","https://openalex.org/W2010941966","https://openalex.org/W2401310550","https://openalex.org/W183576326","https://openalex.org/W171914860","https://openalex.org/W2060317829","https://openalex.org/W4249297485"],"abstract_inverted_index":{"We":[0,42],"study":[1],"the":[2,22,46,62,67,83,87],"convergence":[3,102],"behavior":[4],"of":[5,17,35,39,82,86,103],"a":[6,11,15,26,36,51,55,75,79,100],"stochastic":[7,27,68],"heavy-ball":[8,69],"method":[9],"with":[10],"small":[12,32],"stepsize.":[13],"Under":[14],"change":[16],"time":[18,81],"scale,":[19],"we":[20],"approximate":[21],"discrete":[23],"scheme":[24],"by":[25,112],"differential":[28],"equation":[29],"that":[30,45,60,65],"models":[31],"random":[33],"perturbations":[34],"coupled":[37],"system":[38,48],"nonlinear":[40],"oscillators.":[41],"rigorously":[43],"show":[44],"perturbed":[47],"converges":[49],"to":[50,74,90],"local":[52],"minimum":[53],"in":[54],"logarithmic":[56,76],"time.":[57],"This":[58,96],"indicates":[59],"for":[61],"diffusion":[63],"process":[64],"approximates":[66],"method,":[70],"it":[71],"takes":[72],"(up":[73],"factor)":[77],"only":[78],"linear":[80],"square":[84],"root":[85],"inverse":[88],"stepsize":[89],"escape":[91],"from":[92],"all":[93],"saddle":[94],"points.":[95],"results":[97,109],"may":[98],"suggest":[99],"fast":[101],"its":[104],"discrete-time":[105],"counterpart.":[106],"Our":[107],"theoretical":[108],"are":[110],"validated":[111],"numerical":[113],"experiments.":[114]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-01T08:36:08.643496","created_date":"2025-10-10T00:00:00"}
