An alternating direction method of multipliers with a worst-case O(1/n2) convergence rate

[1]  Xiaoming Yuan,et al.  Convergence Analysis of Primal–Dual Based Methods for Total Variation Minimization with Finite Element Approximation , 2018, J. Sci. Comput..

[2]  Antonin Chambolle,et al.  On the ergodic convergence rates of a first-order primal–dual algorithm , 2016, Math. Program..

[3]  Xiaoming Yuan,et al.  On the Optimal Linear Convergence Rate of a Generalized Proximal Point Algorithm , 2016, J. Sci. Comput..

[4]  Xiaoming Yuan,et al.  On non-ergodic convergence rate of Douglas–Rachford alternating direction method of multipliers , 2015, Numerische Mathematik.

[5]  Bingsheng He,et al.  On the Convergence of Primal-Dual Hybrid Gradient Algorithm , 2014, SIAM J. Imaging Sci..

[6]  Xiaoming Yuan,et al.  A Generalized Proximal Point Algorithm and Its Convergence Rate , 2014, SIAM J. Optim..

[7]  Richard G. Baraniuk,et al.  Fast Alternating Direction Optimization Methods , 2014, SIAM J. Imaging Sci..

[8]  Wotao Yin,et al.  Faster Convergence Rates of Relaxed Peaceman-Rachford and ADMM Under Regularity Assumptions , 2014, Math. Oper. Res..

[9]  Damek Davis,et al.  Convergence Rate Analysis of Several Splitting Schemes , 2014, 1406.4834.

[10]  Xiaoming Yuan,et al.  Local Linear Convergence of the Alternating Direction Method of Multipliers for Quadratic Programs , 2013, SIAM J. Numer. Anal..

[11]  Daniel Boley,et al.  Local Linear Convergence of the Alternating Direction Method of Multipliers on Quadratic or Linear Programs , 2013, SIAM J. Optim..

[12]  Renato D. C. Monteiro,et al.  Iteration-Complexity of Block-Decomposition Algorithms and the Alternating Direction Method of Multipliers , 2013, SIAM J. Optim..

[13]  Xiangfeng Wang,et al.  The Linearized Alternating Direction Method of Multipliers for Dantzig Selector , 2012, SIAM J. Sci. Comput..

[14]  Junfeng Yang,et al.  Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization , 2012, Math. Comput..

[15]  Bingsheng He,et al.  On the O(1/n) Convergence Rate of the Douglas-Rachford Alternating Direction Method , 2012, SIAM J. Numer. Anal..

[16]  Antonin Chambolle,et al.  A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging , 2011, Journal of Mathematical Imaging and Vision.

[17]  Heinz H. Bauschke,et al.  Convex Analysis and Monotone Operator Theory in Hilbert Spaces , 2011, CMS Books in Mathematics.

[18]  Stanley Osher,et al.  A Unified Primal-Dual Algorithm Framework Based on Bregman Iteration , 2010, J. Sci. Comput..

[19]  Yaakov Tsaig,et al.  Fast Solution of $\ell _{1}$ -Norm Minimization Problems When the Solution May Be Sparse , 2008, IEEE Transactions on Information Theory.

[20]  Bingsheng He,et al.  A new inexact alternating directions method for monotone variational inequalities , 2002, Math. Program..

[21]  Dimitri P. Bertsekas,et al.  On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators , 1992, Math. Program..

[22]  P. Lions,et al.  Splitting Algorithms for the Sum of Two Nonlinear Operators , 1979 .

[23]  M. Hestenes.  Multiplier and gradient methods , 1969 .

[24]  H. H. Rachford,et al.  On the numerical solution of heat conduction problems in two and three space variables , 1956 .

[25]  Roland Glowinski,et al.  On Alternating Direction Methods of Multipliers: A Historical Perspective , 2014, Modeling, Simulation and Optimization for Science and Technology.

[26]  Y. Nesterov.  Gradient methods for minimizing composite functions , 2013, Math. Program..

[27]  Bingsheng He,et al.  Convergence Analysis of Primal-Dual Algorithms for a Saddle-Point Problem: From Contraction Perspective , 2012, SIAM J. Imaging Sci..

[28]  Arkadi Nemirovski,et al.  Prox-Method with Rate of Convergence O(1/t) for Variational Inequalities with Lipschitz Continuous Monotone Operators and Smooth Convex-Concave Saddle Point Problems , 2004, SIAM J. Optim..

[29]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[30]  Y. Nesterov.  A method for solving the convex programming problem with convergence rate O(1/k^2) , 1983 .

[31]  R. Glowinski,et al.  Sur l'approximation, par éléments finis d'ordre un, et la résolution, par pénalisation-dualité d'une classe de problèmes de Dirichlet non linéaires , 1975 .

[32]  M. Powell.  A method for nonlinear constraints in minimization problems , 1969 .

[33]  J. Moreau.  Proximité et dualité dans un espace hilbertien , 1965 .