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Alternating minimization (AM) procedures are practically efficient in many applications for solving convex and non-convex optimization problems.
On primal and dual approaches for distributed stochastic convex optimization over networks
Dvinskikh, D., Gorbunov, E., Gasnikov, A., Dvurechensky, P., and Uribe, C. A · 1903
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Lin, T., Ho, N., and Jordan, M. I · 1906
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Alternating minimization methods for strongly convex optimization
Tupitsa, N., Dvurechensky, P., Gasnikov, A., and Guminov, S · 1911
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Efficient accelerated coordinate descent methods and faster algorithms for solving linear systems
Lee, Y. T. and Sidford, A · 1922
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Iterative Solution of Nonlinear Equations in Several Variables
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Diagonal equivalence to matrices with prescribed row and column sums. II
Sinkhorn, R · 1974
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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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Parallel and distributed computation: numerical methods , volume 23
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The EM Algorithm and Extensions
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Introductory Lectures on Convex Optimization: a basic course
Nesterov, Y · 2004
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Multimarginal optimal transport by accelerated alternating minimization
Tupitsa, N., Dvurechensky, P., Gasnikov, A., and Uribe, C. A · 2004
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Smooth minimization of non-smooth functions
Nesterov, Y · 2005
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Gradient methods for minimizing composite functions
Nesterov, Y · 2007
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Collaborative filtering for implicit feedback datasets
Hu, Y., Koren, Y., and Volinsky, C · 2008
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Iteratively reweighted least squares minimization for sparse recovery
Daubechies, I., DeVore, R., Fornasier, M., and Güntürk, C. S · 2010
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Efficiency of coordinate descent methods on huge-scale optimization problems
Nesterov, Y · 2010
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Barycenters in the wasserstein space
Agueh, M. and Carlier, G · 2011
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On the convergence of block coordinate descent type methods
Beck, A. and Tetruashvili, L · 2013
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Sinkhorn distances: Lightspeed computation of optimal transport
Cuturi, M · 2013
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On the nonasymptotic convergence of cyclic coordinate descent methods
Saha, A. and Tewari, A · 2013
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Feedback prediction for blogs
Buza, K · 2014
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Fast computation of wasserstein barycenters
Cuturi, M. and Doucet, A · 2014
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An accelerated proximal coordinate gradient method
Lin, Q., Lu, Z., and Xiao, L · 2014
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Accelerated proximal stochastic dual coordinate ascent for regularized loss minimization
Shalev-Shwartz, S. and Zhang, T · 2014
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On the convergence of alternating minimization for convex programming with applications to iteratively reweighted least squares and decomposition schemes
Beck, A · 2015
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Fast discrete distribution clustering using wasserstein barycenter with sparse support
Ye, J., Wu, P., Wang, J. Z., and Li, J · 2017
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Smooth and sparse optimal transport
Blondel, M., Seguy, V., and Rolet, A · 2018
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Stochastic Wasserstein barycenters
Claici, S., Chien, E., and Solomon, J · 2018
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Decentralize and randomize: Faster algorithm for Wasserstein barycenters
Dvurechensky, P., Dvinskikh, D., Gasnikov, A., Uribe, C. A., and Nedić, A · 2018
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Quadratically regularized optimal transport on graphs
Essid, M. and Solomon, J · 2018
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Accelerating greedy coordinate descent methods
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Benamou, J.-D., Carlier, G., Cuturi, M., Nenna, L., and Peyré, G · 2015
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Accelerated, parallel, and proximal coordinate descent
Fercoq, O. and Richtárik, P · 2015
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Efficiency of the accelerated coordinate descent method on structured optimization problems
Nesterov, Y. and Stich, S. U · 2015
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Improved iteration complexity bounds of cyclic block coordinate descent for convex problems
Sun, R. and Hong, M · 2015
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Even faster accelerated coordinate descent using non-uniform sampling
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Convergence of an alternating maximization procedure
Andresen, A. and Spokoiny, V · 2016
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Fast primal-dual gradient method for strongly convex minimization problems with linear constraints
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Distributed computation of Wasserstein barycenters over networks
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A Fast Globally Linearly Convergent Algorithm for the Computation of Wasserstein Barycenters
Yang, L., Li, J., Sun, D., and Toh, K.-C · 2018
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