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This paper proposes and establishes the iteration-complexity of an inexact proximal accelerated augmented Lagrangian (IPAAL) method for solving linearly constrained smooth nonconvex composite optimization problems.
Augmented Lagrangians and applications of the proximal point algorithm in convex programming
R. T. Rockafellar · 1976
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Constrained optimization and Lagrange multiplier methods
D. P. Bertsekas · 1982
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Introductory lectures on convex optimization : a basic course
Y. E. Nesterov · 2004
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Cubic regularization of newton method and its global performance
Y.E. Nesterov and B.T. Polyak · 2006
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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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On the complexity of steepest descent, Newton’s and regularized Newton’s methods for nonconvex unconstrained optimization problems
C. Cartis, N. Gould, and P. Toint · 2010
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A first-order smoothed penalty method for compressed sensing
N.S. Aybat and G. Iyengar · 2011
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A first-order augmented Lagrangian method for compressed sensing
N.S. Aybat and G. Iyengar · 2012
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Iteration-complexity of a Newton proximal extragradient method for monotone variational inequalities and inclusion problems
R.D.C. Monteiro and B.F. Svaiter · 2012
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Gradient methods for minimizing composite functions
Y. Nesterov · 2012
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Iteration-complexity of first-order penalty methods for convex programming
G. Lan and R. D. C. Monteiro · 2013
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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 · 2013
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Optimal primal-dual methods for a class of saddle point problems
Y. Chen, G. Lan, and Y. Ouyang · 2014
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Accelerating block-decomposition first-order methods for solving composite saddle-point and two-player Nash equilibrium problems
Y. He and R. D. C. Monteiro · 2015
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Accelerated proximal gradient methods for nonconvex programming
H. Li and Z. Lin · 2015
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The rate of convergence of Nesterov's accelerated forward-backward method is actually faster than 1 / k 2 1/k^{2}
H. Attouch and J. Peypouquet · 2016
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Accelerated gradient methods for nonconvex nonlinear and stochastic programming
S. Ghadimi and G. Lan · 2016
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An accelerated HPE-type algorithm for a class of composite convex-concave saddle-point problems
Y. He and R. D. C. Monteiro · 2016
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Stochastic first-order methods for convex and nonconvex functional constrained optimization
D. Boob, Q. Deng, and G. Lan · 2019
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Efficiency of minimizing compositions of convex functions and smooth maps
D. Drusvyatskiy and C. Paquette · 2019
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Generalized uniformly optimal methods for nonlinear programming
S. Ghadimi, G. Lan, and H. Zhang · 2019
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Convergence rate bounds for a proximal admm with over-relaxation stepsize parameter for solving nonconvex linearly constrained problems
M.L.N. Gonçalves, J.G. Melo, and R.D.C. Monteiro · 2019
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Perturbed proximal primal–dual algorithm for nonconvex nonsmooth optimization
D. Hajinezhad1 and M. Hong · 2019
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M. Hong · 2016
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Iteration-complexity of first-order augmented Lagrangian methods for convex programming
G. Lan and R. D. C. Monteiro · 2016
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An adaptive accelerated first-order method for convex optimization
R. D. C. Monteiro, Ortiz, and Benar F. Svaiter · 2016
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An accelerated non-euclidean hybrid proximal extragradient-type algorithm for convex-concave saddle-point problems
O. Kolossoski and R. D. C. Monteiro · 2017
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Complexity of first-order inexact Lagrangian and penalty methods for conic convex programming
I. Necoara, A. Patrascu, and F. Glineur · 2017
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Adaptive inexact fast augmented Lagrangian methods for constrained convex optimization
A. Patrascu, I. Necoara, and Q. Tran-Dinh · 2017
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Accelerated methods for nonconvex optimization
Yair Carmon, John C. Duchi, Oliver Hinder, and Aaron Sidford · 2018
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Structured nonconvex and nonsmooth optimization algorithms and iteration complexity analysis
B. Jiang, T. Lin, S. Ma, and S. Zhang · 2019
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Complexity of a quadratic penalty accelerated inexact proximal point method for solving linearly constrained nonconvex composite programs
W. Kong, J.G. Melo, and R.D.C. Monteiro · 2019
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An accelerated inexact proximal point method for solving nonconvex-concave min-max problems
W Kong and R.D.C. Monteiro · 2019
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An efficient adaptive accelerated inexact proximal point method for solving linearly constrained nonconvex composite problems
Weiwei Kong, Jefferson G. Melo, and Renato D. C. Monteiro · 2019
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First-order inexact augmented Lagrangian methods for convex and nonconvex programs: nonergodic convergence and iteration complexity
Z. Li and Y. Xu · 2019
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Inexact proximal-point penalty methods for non-convex optimization with non-convex constraints
Q. Lin, R. Ma, and Y. Xu · 2019
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On the nonergodic convergence rate of an inexact augmented Lagrangian framework for composite convex programming
Y.F. Liu, X. Liu, and S. Ma · 2019
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Iteration complexity of inexact augmented lagrangian methods for constrained convex programming
Yangyang Xu · 2019
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