{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T15:27:15Z","timestamp":1777994835894,"version":"3.51.4"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"16","license":[{"start":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T00:00:00Z","timestamp":1579305600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T00:00:00Z","timestamp":1579305600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No. 61976243"],"award-info":[{"award-number":["No. 61976243"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No. 61971458"],"award-info":[{"award-number":["No. 61971458"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No. U1604155"],"award-info":[{"award-number":["No. U1604155"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2020,8]]},"DOI":"10.1007\/s00521-020-04718-9","type":"journal-article","created":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T18:02:10Z","timestamp":1579370530000},"page":"12671-12684","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":43,"title":["A Randomized Block-Coordinate Adam online learning optimization algorithm"],"prefix":"10.1007","volume":"32","author":[{"given":"Yangfan","family":"Zhou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2523-1089","authenticated-orcid":false,"given":"Mingchuan","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junlong","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruijuan","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingtao","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,1,18]]},"reference":[{"key":"4718_CR1","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1016\/j.future.2017.07.030","volume":"81","author":"M Zhang","year":"2018","unstructured":"Zhang M, Yang M, Wu Q, Zheng R, Zhu J (2018) Smart perception and autonomic optimization: a novel bio-inspired hybrid routing protocol for MANETs. Fut Gen Comput Syst 81:505\u2013513","journal-title":"Fut Gen Comput Syst"},{"issue":"6","key":"4718_CR2","doi-asserted-by":"publisher","first-page":"1926","DOI":"10.3390\/s18061926","volume":"18","author":"Z Ai","year":"2018","unstructured":"Ai Z, Zhou Y, Song F (2018) A smart collaborative routing protocol for reliable data diffusion in IoT scenarios. Sensors 18(6):1926","journal-title":"Sensors"},{"issue":"3","key":"4718_CR3","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1109\/MNET.2016.7474343","volume":"30","author":"H Zhang","year":"2016","unstructured":"Zhang H, Quan W, Chao H, Qiao C (2016) Smart identifier network: a collaborative architecture for the future internet. IEEE Netw 30(3):46\u201351","journal-title":"IEEE Netw"},{"issue":"1","key":"4718_CR4","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1109\/MNET.2018.1800187","volume":"33","author":"F Song","year":"2019","unstructured":"Song F, Zhou Y, Chang L, Zhang H (2019) Modeling space-terrestrial integrated networks with smart collaborative theory. IEEE Netw 33(1):51\u201357","journal-title":"IEEE Netw"},{"issue":"12","key":"4718_CR5","doi-asserted-by":"publisher","first-page":"2879","DOI":"10.1109\/TIP.2007.909412","volume":"16","author":"S Klein","year":"2008","unstructured":"Klein S, Staring M, Pluim JPW (2008) Evaluation of optimization methods for nonrigid medical image registration using mutual information and B-splines. IEEE Trans Image Process 16(12):2879\u20132890","journal-title":"IEEE Trans Image Process"},{"key":"4718_CR6","doi-asserted-by":"publisher","first-page":"653","DOI":"10.1109\/LWC.2018.2879514","volume":"8","author":"W Quan","year":"2018","unstructured":"Quan W, Cheng N, Qin M, Zhang H, Chan HA, Shen X (2018) Adaptive transmission control for software defined vehicular networks. IEEE Wirel Commun Lett Commun Lett 8:653\u2013656","journal-title":"IEEE Wirel Commun Lett Commun Lett"},{"issue":"1","key":"4718_CR7","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1109\/TSP.2016.2617829","volume":"65","author":"A Mokhtari","year":"2017","unstructured":"Mokhtari A, Ling Q, Ribeiro A (2017) Network Newton distributed optimization methods. IEEE Trans Signal Process 65(1):146\u2013161","journal-title":"IEEE Trans Signal Process"},{"issue":"9","key":"4718_CR8","doi-asserted-by":"publisher","first-page":"4483","DOI":"10.1109\/TAC.2017.2671377","volume":"62","author":"AS Bijral","year":"2017","unstructured":"Bijral AS, Sarwate AD, Srebro N (2017) Data-dependent convergence for consensus stochastic optimization. IEEE Trans Autom Control 62(9):4483\u20134498","journal-title":"IEEE Trans Autom Control"},{"key":"4718_CR9","unstructured":"Li Y, Liang Y (2018) Learning overparameterized neural networks via stochastic gradient descent on structured data. In: NIPS, Montreal, Canada, Dec 2018, pp 8157\u20138166"},{"issue":"2","key":"4718_CR10","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1109\/TMI.2015.2476354","volume":"35","author":"Y Qiao","year":"2016","unstructured":"Qiao Y, Lew BV, Lelieveldt BPF, Staring M (2016) Fast automatic step size estimation for gradient descent optimization of image registration. IEEE Trans Med Imaging 35(2):391\u2013403","journal-title":"IEEE Trans Med Imaging"},{"issue":"2","key":"4718_CR11","doi-asserted-by":"publisher","first-page":"324","DOI":"10.1109\/TFUZZ.2013.2254492","volume":"22","author":"WY Cheng","year":"2014","unstructured":"Cheng WY, Juang CF (2014) A fuzzy model with online incremental SVM and margin-selective gradient descent learning for classification problems. IEEE Trans Fuzzy Syst 22(2):324\u2013337","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"5","key":"4718_CR12","doi-asserted-by":"publisher","first-page":"1256","DOI":"10.1109\/TSP.2014.2301135","volume":"62","author":"R Arablouei","year":"2014","unstructured":"Arablouei R, Werner S, Dogancay K (2014) Analysis of the gradient-descent total least-squares adaptive filtering algorithm. IEEE Trans Signal Process 62(5):1256\u20131264","journal-title":"IEEE Trans Signal Process"},{"key":"4718_CR13","doi-asserted-by":"crossref","unstructured":"Shi S, Wang Q, Chu X, Li B (2018) A DAG model of synchronous stochastic gradient descent in distributed deep learning. In: ICPADS, Singapore, Dec 2018, pp 425\u2013432","DOI":"10.1109\/PADSW.2018.8644932"},{"key":"4718_CR14","unstructured":"Lee C, Cho K, Kang W (September 2018) Directional analysis of stochastic gradient descent via von Mises\u2013Fisher distributions in deep learning. [Online]. Available: arXiv:1810.00150, Initial submission"},{"issue":"11","key":"4718_CR15","doi-asserted-by":"publisher","first-page":"5974","DOI":"10.1109\/TAC.2017.2705559","volume":"62","author":"K Cohen","year":"2017","unstructured":"Cohen K, Nedi\u0107 A, Srikant R (2017) On projected stochastic gradient descent algorithm with weighted averaging for least squares regression. IEEE Trans Autom Control 62(11):5974\u20135981","journal-title":"IEEE Trans Autom Control"},{"key":"4718_CR16","doi-asserted-by":"crossref","unstructured":"Zhou F, Cong GJ (2018) On the convergence properties of a $$k$$-step averaging stochastic gradient descent algorithm for nonconvex optimization. In: IJCAI, Stockholm, Sweden, pp 3219\u20133227, July 2018","DOI":"10.24963\/ijcai.2018\/447"},{"key":"4718_CR17","doi-asserted-by":"crossref","unstructured":"Shen ZB, Qian H, Mu TZ, Zhang C (2017) Accelerated doubly stochastic gradient algorithm for large-scale empirical risk minimization. In: IJCAI, Melbourne, Australia, Aug 2017, pp 2715\u20132721","DOI":"10.24963\/ijcai.2017\/378"},{"key":"4718_CR18","first-page":"2121","volume":"12","author":"J Duchi","year":"2011","unstructured":"Duchi J, Hazan E, Singer Y (2011) Adaptive subgradient methods for online learning and stochastic optimization. J Mach Learn Res 12:2121\u20132159","journal-title":"J Mach Learn Res"},{"key":"4718_CR19","unstructured":"Zeiler MD (2012) ADADELTA: an adaptive learning rate method (online) Dec 2012, Available: arXiv:1212.5701 Initial submission."},{"key":"4718_CR20","unstructured":"Tieleman T, Hinton G (2012) RmsProp: divide the gradient by a running average of its recent magnitude. In: COURSERA: neural networks for machine learning"},{"key":"4718_CR21","unstructured":"Kingma DP, Ba JL (2015) Adam: a method for stochastic optimization. In: ICLR, San Diego, America, May 2015"},{"key":"4718_CR22","unstructured":"Ruder S (2016) An overview of gradient descent optimization algorithms (online) , Sept 2016. Available: arXiv:1609.04747, Initial submission."},{"key":"4718_CR23","unstructured":"Dozat T (2016) Incorporating Nesterov momentum into Adam. In: ICLR, San Juan, Puerto Rico, May 2016"},{"key":"4718_CR24","unstructured":"Shazeer N, Stern M (2018) Adafactor: adaptive learning rates with sublinear memory cost. In: ICML, Stockholm, Sweden, PMLR, July 2018, pp 4596\u20134604"},{"key":"4718_CR25","unstructured":"Reddi SJ, Kale S, Kumar S (2018) On the convergence of Adam and beyond. In: ICLR, Vancouver, Canada, May 2018"},{"key":"4718_CR26","unstructured":"Zhang JW, Cui LM, Gouza FB (2018) GADAM: genetic-evolutionary ADAM for deep neural network optimization (online) May 2018. Available: arXiv:1805.07500, Initial submission"},{"key":"4718_CR27","unstructured":"Zaheer M, Reddi S, Sachan D, Sachan S, Kumar S (2018) Adaptive methods for Nonconvex optimization. In: NIPS, Montreal, Canada, Curran Associates, Inc, Dec 2018"},{"key":"4718_CR28","first-page":"372","volume":"27","author":"YE Nesterov","year":"1983","unstructured":"Nesterov YE (1983) A method of solving a convex programming problem with convergence rate $$O(1\/{k^{2}})$$. Soviet Mathematics Doklady 27:372\u2013376","journal-title":"Soviet Mathematics Doklady"},{"key":"4718_CR29","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8853-9","volume-title":"Introductory lectures on convex optimization: a basic course","author":"Y Nesterov","year":"2004","unstructured":"Nesterov Y (2004) Introductory lectures on convex optimization: a basic course. Springer, Boston, MA"},{"key":"4718_CR30","unstructured":"Khan ME, Nielsen D, Tangkaratt V, Lin W, Gal Y, Srivastava A (2018) Fast and scalable bayesian deep learning by weight-perturbation in Adam. In: ICML, Stockholm, Sweden, PMLR, July 2018"},{"issue":"3","key":"4718_CR31","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1023\/A:1017501703105","volume":"109","author":"P Tseng","year":"2001","unstructured":"Tseng P (2001) Convergence of a block coordinate descent method for nondifferentiable minimization. J Optim Theory Appl 109(3):475\u2013494","journal-title":"J Optim Theory Appl"},{"issue":"2","key":"4718_CR32","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1137\/100802001","volume":"22","author":"Y Nesterov","year":"2012","unstructured":"Nesterov Y (2012) Efficiency of coordinate descent methods on huge-scale optimization problems. SIAM J Optim 22(2):341\u2013364","journal-title":"SIAM J Optim"},{"issue":"9","key":"4718_CR33","doi-asserted-by":"publisher","first-page":"1927","DOI":"10.1109\/TNNLS.2014.2361159","volume":"26","author":"EL Hu","year":"2015","unstructured":"Hu EL, Kwok JT (2015) Scalable nonparametric low-rank kernel learning using block coordinate descent. IEEE Trans Neural Netw Learn Syst 26(9):1927\u20131938","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"4718_CR34","unstructured":"Zhao T, Yu M, Wang Y, Arora R, Liu H (2014) Accelerated mini-batch randomized block coordinate descent method. In: NIPS, Montreal, Canada, Curran Associates, Inc., Dec 2014, pp 3329\u20133337"},{"key":"4718_CR35","unstructured":"Simon LJ, Martin J, Schmidt M, Pletscher P (2013) Block-coordinate frank-wolfe optimization for structural SVMs. In: ICML, Atlanta, America, PMLR, June 2013, pp 53\u201361"},{"key":"4718_CR36","doi-asserted-by":"crossref","unstructured":"Singh C, Nedi\u0107 A, Srikant R (2014) Random block-coordinate gradient projection algorithms. In: CDC, Los Angeles, America, IEEE, Dec 2014, pp 185\u2013190","DOI":"10.1109\/CDC.2014.7039379"},{"key":"4718_CR37","unstructured":"Xie TY, Liu B, Xu YY, Ghavamzadeh M, Chow Y, Lyu D (2018) A block coordinate ascent algorithm for mean-variance optimization. In: NIPS, Montreal, Canada, Curran Associates, Inc., Dec 2018, pp 1073\u20131083"},{"key":"4718_CR38","unstructured":"Cohen A, Hasidim A, Koren T, Lazic N, Mansour Y, Talwar K (2018) Online linear quadratic control. In: ICML, Stockholm, Sweden, PMLR, July 2018, pp 1029\u20131038"},{"key":"4718_CR39","unstructured":"Wang Y, Yao Q, James TK, Lionel MN (2018) Online convolutional sparse coding with sample-dependent dictionary. In: ICML, Stockholm, Sweden, PMLR, July 2018, pp 5209\u20135218"},{"key":"4718_CR40","unstructured":"Zhang W, Zhao P, Zhu W, Hoi SCH, Zhang T (2017) Projection-free distributed online learning in networks. In: ICML, Sydney, Australia, PMLR, Aug 2017, pp 4054\u20134062"},{"key":"4718_CR41","doi-asserted-by":"publisher","DOI":"10.1109\/JIOT.2019.2919562","author":"M Zhang","year":"2019","unstructured":"Zhang M, Quan W, Cheng N, Wu Q, Zhu J, Zheng R, Li K (2019) Distributed conditional gradient online learning for IoT optimization. IEEE Intern Things J. https:\/\/doi.org\/10.1109\/JIOT.2019.2919562","journal-title":"IEEE Intern Things J"},{"key":"4718_CR42","unstructured":"Nedi\u0107 A, Lee S, Raginsky M (2015) Decentralized online optimization with global objectives and local communication. In: ACC, America, July 2015, pp 4497\u20134503"},{"issue":"1","key":"4718_CR43","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1109\/TSIPN.2018.2797806","volume":"4","author":"J Zhu","year":"2018","unstructured":"Zhu J, Xu C, Guan J, Wu DO (2018) Differentially private distributed online algorithms over time-varying directed networks. IEEE Trans Signal Inf Process Netw 4(1):4\u201317","journal-title":"IEEE Trans Signal Inf Process Netw"},{"key":"4718_CR44","unstructured":"Zinkevich M (2003) Online convex programming and generalized infinitesimal gradient ascent. In: ICML, Washington DC, America, AAAI Press, Aug 2003, pp 928\u2013936"},{"key":"4718_CR45","volume-title":"Convex optimization","author":"S Boyd","year":"2013","unstructured":"Boyd S, Vandenberghe L (2013) Convex optimization. Cambridge University Press, Cambridge"},{"key":"4718_CR46","volume-title":"Probability: theory and examples","author":"R Durrett","year":"2005","unstructured":"Durrett R (2005) Probability: theory and examples, 3rd edn. Cengage Learning, Singapore","edition":"3"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-020-04718-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-020-04718-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-020-04718-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,1,17]],"date-time":"2021-01-17T00:19:45Z","timestamp":1610842785000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-020-04718-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,18]]},"references-count":46,"journal-issue":{"issue":"16","published-print":{"date-parts":[[2020,8]]}},"alternative-id":["4718"],"URL":"https:\/\/doi.org\/10.1007\/s00521-020-04718-9","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1,18]]},"assertion":[{"value":"27 June 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 January 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 January 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that there is no conflict of interests regarding the publication of this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}}]}}