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Block Coordinate Update (BCU) methods enjoy low per-update computational complexity because every time only one or a few block variables would need to be updated among possibly a large number of blocks.
Portfolio selection
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Sur l’approximation, par eléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de dirichlet non linéaires
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A dual algorithm for the solution of nonlinear variational problems via finite element approximation
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A method of solving a convex programming problem with convergence rate O ( 1 / k 2 ) {O}(1/k^{2})
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Support-vector networks
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Atomic decomposition by basis pursuit
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Alternating direction method with gaussian back substitution for separable convex programming
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On the O ( 1 / n ) O(1/n) convergence rate of the Douglas-Rachford alternating direction method
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Efficiency of coordinate descent methods on huge-scale optimization problems
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Parallel coordinate descent methods for big data optimization
P. Richtárik and M. Takáč · 2012
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Local linear convergence of the alternating direction method of multipliers on quadratic or linear programs
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Penalized and constrained regression
G. M. James, C. Paulson, and P. Rusmevichientong · 2013
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R. D. Monteiro and B. F. Svaiter · 2013
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Gradient methods for minimizing composite functions
Y. Nesterov · 2013
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The direct extension of admm for three-block separable convex minimization models is convergent when one function is strongly convex
X. Cai, D. Han, and X. Yuan · 2014
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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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On the global linear convergence of the admm with multiblock variables
T. Lin, S. Ma, and S. Zhang · 2015
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On the complexity analysis of randomized block-coordinate descent methods
Z. Lu and L. Xiao · 2015
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An accelerated linearized alternating direction method of multipliers
Y. Ouyang, Y. Chen, G. Lan, and E. Pasiliao Jr · 2015
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Accelerated douglas-rachford methods for the solution of convex-concave saddle-point problems
K. Bredies and H. Sun · 2016
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The direct extension of admm for multi-block convex minimization problems is not necessarily convergent
C. Chen, B. He, Y. Ye, and X. Yuan · 2016
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C. Dang and G. Lan · 2014
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Fast alternating direction optimization methods
T. Goldstein, B. O’Donoghue, S. Setzer, and R. Baraniuk · 2014
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A class of randomized primal-dual algorithms for distributed optimization
J.-C. Pesquet and A. Repetti · 2014
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Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function
P. Richtárik and M. Takáč · 2014
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Stochastic quasi-fejér block-coordinate fixed point iterations with random sweeping
P. L. Combettes and J.-C. Pesquet · 2015
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On the global and linear convergence of the generalized alternating direction method of multipliers
W. Deng and W. Yin · 2015
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First-order algorithms for convex optimization with nonseparable objective and coupled constraints
X. Gao and S.-Z. Zhang · 2015
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W. Deng, M.-J. Lai, Z. Peng, and W. Yin · 2016
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Randomized primal-dual proximal block coordinate updates
X. Gao, Y. Xu, and S. Zhang · 2016
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H. Li and Z. Lin · 2016
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Coordinate friendly structures, algorithms and applications
Z. Peng, T. Wu, Y. Xu, M. Yan, and W. Yin · 2016
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Arock: an algorithmic framework for asynchronous parallel coordinate updates
Z. Peng, Y. Xu, M. Yan, and W. Yin · 2016
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Y. Xu · 2016
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Accelerated first-order primal-dual proximal methods for linearly constrained composite convex programming
Y. Xu · 2017
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Asynchronous parallel primal-dual block update methods
Y. Xu · 2017
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