{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:08:33Z","timestamp":1740132513045,"version":"3.37.3"},"reference-count":64,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"1","license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"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\/100000183","name":"Army Research Office","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008982","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100008982","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Automat. Contr."],"published-print":{"date-parts":[[2023,1]]},"DOI":"10.1109\/tac.2021.3137147","type":"journal-article","created":{"date-parts":[[2021,12,21]],"date-time":"2021-12-21T20:45:36Z","timestamp":1640119536000},"page":"80-95","source":"Crossref","is-referenced-by-count":0,"title":["On the Absence of Spurious Local Trajectories in Time-Varying Nonconvex Optimization"],"prefix":"10.1109","volume":"68","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7986-3148","authenticated-orcid":false,"given":"Salar","family":"Fattahi","sequence":"first","affiliation":[{"name":"University of Michigan, Ann Arbor, MI, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2882-8697","authenticated-orcid":false,"given":"Cedric","family":"Josz","sequence":"additional","affiliation":[{"name":"Columbia University, New York, NY, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1521-7566","authenticated-orcid":false,"given":"Yuhao","family":"Ding","sequence":"additional","affiliation":[{"name":"University of California, Berkeley, Berkeley, CA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7494-3050","authenticated-orcid":false,"given":"Reza","family":"Mohammadi","sequence":"additional","affiliation":[{"name":"BioSensics, Newton, MA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4294-1338","authenticated-orcid":false,"given":"Javad","family":"Lavaei","sequence":"additional","affiliation":[{"name":"University of California, Berkeley, Berkeley, CA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7177-7712","authenticated-orcid":false,"given":"Somayeh","family":"Sojoudi","sequence":"additional","affiliation":[{"name":"University of California, Berkeley, Berkeley, CA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1109\/CCTA41146.2020.9206163"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/TCNS.2014.2309732"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1002\/0471427950"},{"key":"ref4","first-page":"3585","article-title":"Dynamic matrix recovery from incomplete observations under an exact low-rank constraint","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Xu","year":"2016"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/CAMSAP.2017.8313104"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1145\/2939672.2939878"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1163\/156855307780108277"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2020.3003156"},{"key":"ref9","first-page":"3873","article-title":"Global optimality of local search for low rank matrix recovery","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Bhojanapalli","year":"2016"},{"key":"ref10","first-page":"2973","article-title":"Matrix completion has no spurious local minimum","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Ge","year":"2016"},{"key":"ref11","first-page":"1","article-title":"Sharp restricted isometry bounds for the inexistence of spurious local minima in nonconvex matrix recovery","volume":"20","author":"Zhang","year":"2019","journal-title":"J. Mach. Learn. Res."},{"key":"ref12","article-title":"Exact guarantees on the absence of spurious local minima for non-negative robust principal component analysis","volume-title":"J. Mach. Learn. Res.","author":"Fattahi","year":"2020"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20132"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2009.2035722"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-009-9045-5"},{"key":"ref16","first-page":"6389","article-title":"Visualizing the loss landscape of neural nets","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Li","year":"2018"},{"key":"ref17","first-page":"1233","article-title":"No spurious local minima in nonconvex low rank problems: A unified geometric analysis","volume-title":"Proc. 34th Int. Conf. Mach. Learn.","author":"Ge","year":"2017"},{"key":"ref18","first-page":"2441","article-title":"A theory on the absence of spurious solutions for nonconvex and nonsmooth optimization","volume-title":"Proc. Adv. neural Inf. Process. Syst.","author":"Josz","year":"2018"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2016.2632162"},{"key":"ref20","first-page":"2698","article-title":"An alternative view: When does SGD escape local minima?","volume-title":"Proc. 35th Int. Conf. Mach. Learn.","author":"Kleinberg","year":"2018"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1109\/TSG.2017.2704922"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1137\/20m1371063"},{"key":"ref23","first-page":"2510","article-title":"A differential equation for modeling Nesterovs accelerated gradient method: Theory and insights","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Su","year":"2014"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1614734113"},{"key":"ref25","first-page":"3900","article-title":"Direct Runge-Kutta discretization achieves acceleration","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Zhang","year":"2018"},{"key":"ref26","first-page":"6571","article-title":"Neural ordinary differential equations","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Chen","year":"2018"},{"key":"ref27","first-page":"1109","article-title":"Integration methods and optimization algorithms","volume-title":"Proc. 31st Int. Conf. Neural Inf. Process. Syst.","author":"Scieur","year":"2017"},{"key":"ref28","first-page":"3126","article-title":"Global convergence of Langevin dynamics based algorithms for nonconvex optimization","volume-title":"Proc. 32nd Int. Conf. Neural Inf. Process. Syst.","author":"Xu","year":"2018"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2015.12.030"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1109\/9.701102"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6911(99)00039-0"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2006.06.045"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1109\/TPWRS.2013.2274577"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1109\/TPWRS.2011.2160974"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.13.5.344"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1038\/sj.jors.2600425"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1145\/1553374.1553407"},{"key":"ref38","first-page":"1246","article-title":"Gradient descent only converges to minimizers","volume-title":"Proc. Conf. Learn. Theory","author":"Lee","year":"2016"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-018-09409-5"},{"volume-title":"Numerical Optimization","year":"2006","author":"Nocedal","key":"ref40"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804441"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-18842-3"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-004-0559-y"},{"volume-title":"Theory of Ordinary Differential Equations","year":"1955","author":"Coddington","key":"ref44"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1002\/9781119121534"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1007\/BF01588311"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1080\/10556789408805567"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012902419977"},{"key":"ref49","first-page":"184","article-title":"An algorithm for constrained maximization in nonlinear programming","volume":"17","author":"Tanabe","year":"1974","journal-title":"J. Oper. Res. Soc. Jpn."},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1017\/S0025557200179598"},{"key":"ref51","article-title":"On large-batch training for deep learning: Generalization gap and sharp minima","volume-title":"Proc. 5th Int. Conf. Learn. Representations","author":"Keskar","year":"2017"},{"key":"ref52","volume-title":"Nonlinear Syst.","volume":"3","author":"Khalil","year":"2002"},{"key":"ref53","first-page":"2:12:12","article-title":"Gradient descent only converges to minimizers: Non-isolated critical points and invariant regions","volume-title":"Proc. 8th Innov. Theor. Comput. Sci. Conf.","author":"Panageas","year":"2017"},{"article-title":"Active strict saddles in nonsmooth optimization","year":"2019","author":"Davis","key":"ref54"},{"key":"ref55","first-page":"1724","article-title":"How to escape saddle points efficiently","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Jin","year":"2017"},{"key":"ref56","first-page":"5987","article-title":"Efficiently escaping saddle points on manifolds","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Criscitiello","year":"2019"},{"key":"ref57","volume-title":"Ordinary Differential Equations With Applications","volume":"34","author":"Chicone","year":"2006"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(98)00019-3"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1002\/aic.690460317"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2016.02.039"},{"volume-title":"Real and Complex Analysis","year":"2006","author":"Rudin","key":"ref61"},{"key":"ref62","volume-title":"Principles of Mathematical Analysis","volume":"3","author":"Rudin","year":"1964"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.18.11.620"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1109\/TCNS.2021.3084039"}],"container-title":["IEEE Transactions on Automatic Control"],"original-title":[],"link":[{"URL":"https:\/\/ieeexplore.ieee.org\/ielam\/9\/10002258\/9658210-aam.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/9\/10002258\/09658210.pdf?arnumber=9658210","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,10]],"date-time":"2024-01-10T00:30:19Z","timestamp":1704846619000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9658210\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1]]},"references-count":64,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.1109\/tac.2021.3137147","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":[[2023,1]]}}}