Block-Wise ADMM with a Relaxation Factor for Multiple-Block Convex Programming

[1]  Bingsheng He,et al.  The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent , 2014, Mathematical Programming.

[2]  Bingsheng He,et al.  Block-wise Alternating Direction Method of Multipliers for Multiple-block Convex Programming and Beyond , 2015 .

[3]  Bingsheng He,et al.  A Strictly Contractive Peaceman-Rachford Splitting Method for Convex Programming , 2014, SIAM J. Optim..

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

[5]  Jonathan Eckstein.  Augmented Lagrangian and Alternating Direction Methods for Convex Optimization: A Tutorial and Some Illustrative Computational Results , 2012 .

[6]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[7]  Wotao Yin,et al.  Alternating direction augmented Lagrangian methods for semidefinite programming , 2010, Math. Program. Comput..

[8]  Y. Nesterov.  Gradient methods for minimizing composite objective function , 2007 .

[9]  M. H. Xu.  Proximal Alternating Directions Method for Structured Variational Inequalities , 2007 .

[10]  F. Facchinei,et al.  Finite-Dimensional Variational Inequalities and Complementarity Problems , 2003 .

[11]  Bingsheng He,et al.  Some convergence properties of a method of multipliers for linearly constrained monotone variational inequalities , 1998, Oper. Res. Lett..

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

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

[14]  R. Tyrrell Rockafellar,et al.  Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming , 1976, Math. Oper. Res..

[15]  B. Mercier,et al.  A dual algorithm for the solution of nonlinear variational problems via finite element approximation , 1976 .

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

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

[18]  H. H. Rachford,et al.  The Numerical Solution of Parabolic and Elliptic Differential Equations , 1955 .