{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:57:40Z","timestamp":1760245060013,"version":"3.37.3"},"reference-count":57,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"8","license":[{"start":{"date-parts":[[2022,8,1]],"date-time":"2022-08-01T00:00:00Z","timestamp":1659312000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2022,8,1]],"date-time":"2022-08-01T00:00:00Z","timestamp":1659312000000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2022,8,1]],"date-time":"2022-08-01T00:00:00Z","timestamp":1659312000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2022,8,1]],"date-time":"2022-08-01T00:00:00Z","timestamp":1659312000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014036","name":"Multidisciplinary University Research Initiative","doi-asserted-by":"publisher","award":["FA9550-18-1-0502"],"award-info":[{"award-number":["FA9550-18-1-0502"]}],"id":[{"id":"10.13039\/100014036","id-type":"DOI","asserted-by":"publisher"}]},{"name":"NSF","award":["NSF CNS-1837607"],"award-info":[{"award-number":["NSF CNS-1837607"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Automat. Contr."],"published-print":{"date-parts":[[2022,8]]},"DOI":"10.1109\/tac.2021.3111853","type":"journal-article","created":{"date-parts":[[2021,9,10]],"date-time":"2021-09-10T20:06:00Z","timestamp":1631304360000},"page":"3949-3964","source":"Crossref","is-referenced-by-count":7,"title":["Distributed Gradient Flow: Nonsmoothness, Nonconvexity, and Saddle Point Evasion"],"prefix":"10.1109","volume":"67","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1710-5584","authenticated-orcid":false,"given":"Brian","family":"Swenson","sequence":"first","affiliation":[{"name":"Applied Research Laboratory, Pennsylvania State University, State College, PA, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4491-4096","authenticated-orcid":false,"given":"Ryan","family":"Murray","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, North Carolina State University, Raleigh, NC, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2062-131X","authenticated-orcid":false,"given":"H. Vincent","family":"Poor","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8060-5581","authenticated-orcid":false,"given":"Soummya","family":"Kar","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, USA"}]}],"member":"263","reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1109\/TSIPN.2016.2524588"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2012.2228038"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.13140\/RG.2.2.25204.14729"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1561\/2200000058"},{"key":"ref5","first-page":"5330","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Lian","year":"2017"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1145\/3065386"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-018-09409-5"},{"key":"ref8","volume-title":"Ordinary Differential Equations With Applications","volume":"34","author":"Chicone","year":"2006"},{"key":"ref9","doi-asserted-by":"crossref","DOI":"10.1201\/b18333","volume-title":"Measure Theory and Fine Properties of Functions","author":"Evans","year":"2015"},{"key":"ref10","volume-title":"Nonsmooth Analysis and Control Theory","volume":"178","author":"Clarke","year":"2008"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/MCS.2008.919306"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-4848-0_10"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1137\/110848396"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2012.2198470"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2008.2009515"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2006.887293"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2010.2052531"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2012.2209984"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012904439301"},{"key":"ref20","volume-title":"Differential Topology","volume":"33","author":"Hirsch","year":"2012"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1137\/19M1298147"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1137\/130920216"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5700-4"},{"article-title":"Distributed stochastic gradient descent: Nonconvexity, nonsmoothnes, and convergence to local minima","year":"2020","author":"Swenson","key":"ref24"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1137\/17M1139461"},{"key":"ref26","first-page":"1","article-title":"Optimal convergence rates for convex distributed optimization in networks","volume":"20","author":"Scaman","year":"2019","journal-title":"J. Mach. Learn. Res."},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2014.2364096"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2013.2278132"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2010.2041686"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2016.2628807"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2011.2167817"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2014.2298712"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1137\/16M1084316"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2011.2161027"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2017.2752001"},{"key":"ref36","first-page":"1246","article-title":"Gradient descent only converges to minimizers","volume-title":"Proc. Conf. Learn. Theory","author":"Lee","year":"2016"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-019-01374-3"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1145\/3418526"},{"key":"ref39","first-page":"1724","article-title":"How to escape saddle points efficiently","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Jin","year":"2017"},{"key":"ref40","first-page":"1067","article-title":"Gradient descent can take exponential time to escape saddle points","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Du","year":"2017"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2019.2914998"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-018-01357-w"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2017.2648041"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1109\/ALLERTON.2018.8636055"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2019.2943230"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2017.2685559"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1109\/ACSSC.2016.7869154"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1137\/18M121784X"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2021.3050858"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1109\/CDC40024.2019.9029708"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP40776.2020.9054279"},{"first-page":"2020","article-title":"Stochastic gradient Langevin dynamics on a distributed network","author":"Kungurtsev","key":"ref52"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1109\/ALLERTON.2019.8919658"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1090\/cbms\/092"},{"key":"ref55","volume-title":"A Course in Functional Analysis","volume":"96","author":"Conway","year":"2019"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1007\/springerreference_60688"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2021.3111853"}],"container-title":["IEEE Transactions on Automatic Control"],"original-title":[],"link":[{"URL":"https:\/\/ieeexplore.ieee.org\/ielam\/9\/9842389\/9535220-aam.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/9\/9842389\/09535220.pdf?arnumber=9535220","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,12]],"date-time":"2024-01-12T00:06:12Z","timestamp":1705017972000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9535220\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8]]},"references-count":57,"journal-issue":{"issue":"8"},"URL":"https:\/\/doi.org\/10.1109\/tac.2021.3111853","relation":{},"ISSN":["0018-9286","1558-2523","2334-3303"],"issn-type":[{"type":"print","value":"0018-9286"},{"type":"electronic","value":"1558-2523"},{"type":"electronic","value":"2334-3303"}],"subject":[],"published":{"date-parts":[[2022,8]]}}}