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In this paper, we generalize the well-known Nesterov's accelerated gradient (AG) method, originally designed for convex smooth optimization, to solve nonconvex and possibly stochastic optimization problems.
A stochastic approximation method
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Problem complexity and method efficiency in optimization
A. S. Nemirovski and D. Yudin · 1983
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A method for unconstrained convex minimization problem with the rate of convergence O ( 1 / k 2 ) O(1/k^{2})
Y. E. Nesterov · 1983
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Y. E. Nesterov · 2005
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A. M. Law · 2007
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Gradient methods for minimizing composite objective functions
Y. E. Nesterov · 2007
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Recursive trust-region methods for multiscale nonlinear optimization
A. Sartenaer S. Gratton and Ph. L. Toint · 2008
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On accelerated proximal gradient methods for convex-concave optimization
P. Tseng · 2008
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A fast iterative shrinkage-thresholding algorithm for linear inverse problems
A. Beck and M. Teboulle · 2009
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A proximal method for composite minimization
A.S. Lewis and S.J. Wright · 2009
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An accelerated hybrid proximal extragradient method for convex optimization and its implications to second-order methods
R.D.C. Monteiro and B.F. Svaiter · 2011
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Complexity of unconstrained l 2 − l p l_{2}-l_{p} minimization
X. Chen, D. Ge, Z. Wang, and Y. Ye · 2012
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Optimal stochastic approximation algorithms for strongly convex stochastic composite optimization, I: a generic algorithmic framework
S. Ghadimi and G. Lan · 2012
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Stochastic first- and zeroth-order methods for nonconvex stochastic programming
S. Ghadimi and G. Lan · 2012
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An optimal method for stochastic composite optimization
G. Lan · 2012
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Stochastic block mirror descent methods for nonsmooth and stochastic optimization
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Robust stochastic approximation approach to stochastic programming
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On the complexity of steepest descent, newton’s and regularized newton’s methods for nonconvex unconstrained optimization
C. Cartis, N. I. M. Gould, and Ph. L. Toint · 2010
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Optimal stochastic approximation algorithms for strongly convex stochastic composite optimization, II: shrinking procedures and optimal algorithms
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M. Feng, J. E. Mitchell, J.-S. Pang, X. Shen, , and A. W\lx@bibnewblockTechnical report
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C. D. Dang and G. Lan · 2013
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Mini-batch stochastic approximation methods for constrained nonconvex stochastic programming
S. Ghadimi, G. Lan, and H. Zhang · 2013
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Bundle-level type methods uniformly optimal for smooth and non-smooth convex optimization
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Iteration-complexity of first-order augmented lagrangian methods for convex programming
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