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In this paper, a new variant of accelerated gradient descent is proposed.
D. Kim and J.A. Fessler, Generalizing the optimized gradient method for smooth convex minimization , SIAM Journal on Optimization 28 (2018), pp. 1920–1950
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Y. Nesterov, Smooth minimization of non-smooth functions , Mathematical Programming 103 (2005), pp. 127–152
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J. Nocedal and S.J. Wright, Numerical Optimization , 2nd ed., Springer, New York, NY, USA, 2006
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Y. Nesterov, Gradient methods for minimizing composite functions , Mathematical Programming 140 (2013), pp. 125–161. First appeared in 2007 as CORE discussion paper 2007/76
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N. Andrei, 40 conjugate gradient algorithms for unconstrained optimization. a survey on their definition , 2008. https://camo.ici.ro/neculai/p13a08.pdf
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A. Yurtsever, Q. Tran-Dinh, and V. Cevher, A Universal Primal-dual Convex Optimization Framework , in Proceedings of the 28th International Conference on Neural Information Processing Systems , Cambridge, MA, USA. MIT Press, NIPS’15, 2015, pp. 3150–3158
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A. Chernov, P. Dvurechensky, and A. Gasnikov, Fast Primal-Dual Gradient Method for Strongly Convex Minimization Problems with Linear Constraints , in Discrete Optimization and Operations Research: 9th International Conference, DOOR 2016, Vladivostok, Russia, September 19-23, 2016, Proceedings , Y. Kochetov, M. Khachay, V. Beresnev, E. Nurminski, and P. Pardalos, eds. Springer International Publishing, 2016, pp. 391–403
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2009
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Y. Nesterov, How to make the gradients small , Optima 88 (2012), pp. 10–11
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2014
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A. Beck and M. Teboulle, A fast dual proximal gradient algorithm for convex minimization and applications , Operations Research Letters 42 (2014), pp. 1 – 6
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A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization (Lecture Notes) , Personal web-page of A. Nemirovski, 2015, Available at http://www2.isye.gatech.edu/~nemirovs/Lect_ModConvOpt.pdf
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2015
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S. Ghadimi and G. Lan, Accelerated gradient methods for nonconvex nonlinear and stochastic programming , Mathematical Programming 156 (2016), pp. 59–99. Available at http://dx.doi.org/10.1007/s10107-015-0871-8
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E. de Klerk, F. Glineur, and A.B. Taylor, On the worst-case complexity of the gradient method with exact line search for smooth strongly convex functions , Optimization Letters 11 (2017), pp. 1185–1199. Available at https://doi.org/10.1007/s11590-016-1087-4
2017
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2017
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2017
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2018
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2018
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