A Parallel Line Search Subspace Correction Method for Composite Convex Optimization

[1]  Bingsheng He,et al.  On the Proximal Jacobian Decomposition of ALM for Multiple-Block Separable Convex Minimization Problems and Its Relationship to ADMM , 2016, J. Sci. Comput..

[2]  Lin Xiao,et al.  An Accelerated Randomized Proximal Coordinate Gradient Method and its Application to Regularized Empirical Risk Minimization , 2015, SIAM J. Optim..

[3]  K. Toh,et al.  A Schur complement based semi-proximal ADMM for convex quadratic conic programming and extensions , 2014, Mathematical programming.

[4]  Tianyi Lin,et al.  On the Convergence Rate of Multi-Block ADMM , 2014 .

[5]  Zhaosong Lu,et al.  An Accelerated Proximal Coordinate Gradient Method and its Application to Regularized Empirical Risk Minimization , 2014, 1407.1296.

[6]  Peter Richtárik,et al.  Accelerated, Parallel, and Proximal Coordinate Descent , 2013, SIAM J. Optim..

[7]  Wotao Yin,et al.  Parallel Multi-Block ADMM with o(1 / k) Convergence , 2013, Journal of Scientific Computing.

[8]  Ming Yan,et al.  Parallel and distributed sparse optimization , 2013, 2013 Asilomar Conference on Signals, Systems and Computers.

[9]  Zhi-Quan Luo,et al.  Iteration complexity analysis of block coordinate descent methods , 2013, Mathematical Programming.

[10]  Amir Beck,et al.  On the Convergence of Block Coordinate Descent Type Methods , 2013, SIAM J. Optim..

[11]  Shiqian Ma,et al.  Solving Multiple-Block Separable Convex Minimization Problems Using Two-Block Alternating Direction Method of Multipliers , 2013, ArXiv.

[12]  Lin Xiao,et al.  Randomized Block Coordinate Non-Monotone Gradient Method for a Class of Nonlinear Programming , 2013, ArXiv.

[13]  Lin Xiao,et al.  On the complexity analysis of randomized block-coordinate descent methods , 2013, Mathematical Programming.

[14]  Z. Luo,et al.  On the Linear Convergence of a Proximal Gradient Method for a Class of Nonsmooth Convex Minimization Problems , 2013 .

[15]  Carola-Bibiane Schönlieb,et al.  Bregmanized Domain Decomposition for Image Restoration , 2013, J. Sci. Comput..

[16]  Peter Richtárik,et al.  Parallel coordinate descent methods for big data optimization , 2012, Mathematical Programming.

[17]  Ambuj Tewari,et al.  Feature Clustering for Accelerating Parallel Coordinate Descent , 2012, NIPS.

[18]  Wotao Yin,et al.  On the convergence of an active-set method for ℓ1 minimization , 2012, Optim. Methods Softw..

[19]  Carola-Bibiane Schönlieb,et al.  Wavelet Decomposition Method for L2//TV-Image Deblurring , 2012, SIAM J. Imaging Sci..

[20]  Yurii Nesterov,et al.  Efficiency of Coordinate Descent Methods on Huge-Scale Optimization Problems , 2012, SIAM J. Optim..

[21]  Peter Richtárik,et al.  Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function , 2011, Mathematical Programming.

[22]  Joseph K. Bradley,et al.  Parallel Coordinate Descent for L1-Regularized Loss Minimization , 2011, ICML.

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

[24]  Ya-Xiang Yuan,et al.  Optimization Theory and Methods: Nonlinear Programming , 2010 .

[25]  Trevor Hastie,et al.  Regularization Paths for Generalized Linear Models via Coordinate Descent. , 2010, Journal of statistical software.

[26]  Ambuj Tewari,et al.  Stochastic methods for l1 regularized loss minimization , 2009, ICML '09.

[27]  Carola-Bibiane Schönlieb,et al.  A convergent overlapping domain decomposition method for total variation minimization , 2009, Numerische Mathematik.

[28]  Yin Zhang,et al.  Fixed-Point Continuation for l1-Minimization: Methodology and Convergence , 2008, SIAM J. Optim..

[29]  Paul Tseng,et al.  A coordinate gradient descent method for nonsmooth separable minimization , 2008, Math. Program..

[30]  Carola-Bibiane Schönlieb,et al.  Subspace Correction Methods for Total Variation and 1-Minimization , 2007, SIAM J. Numer. Anal..

[31]  M. Fornasier.  Domain decomposition methods for linear inverse problems with sparsity constraints , 2007 .

[32]  S. Sathiya Keerthi,et al.  A simple and efficient algorithm for gene selection using sparse logistic regression , 2003, Bioinform..

[33]  Carsten Carstensen,et al.  Domain decomposition for a non-smooth convex minimization problem and its application to plasticity , 1997, Numer. Linear Algebra Appl..

[34]  Z.-Q. Luo,et al.  Error bounds and convergence analysis of feasible descent methods: a general approach , 1993, Ann. Oper. Res..

[35]  P. Tseng,et al.  On the linear convergence of descent methods for convex essentially smooth minimization , 1992 .

[36]  P. Tseng,et al.  On the convergence of the coordinate descent method for convex differentiable minimization , 1992 .

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

[38]  Xiaoming Yuan,et al.  On the Direct Extension of ADMM for Multi-block Separable Convex Programming and Beyond : From Variational Inequality Perspective , 2014 .

[39]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[40]  Ya-Xiang Yuan,et al.  Optimization theory and methods , 2006 .

[41]  Jinchao Xu,et al.  Global and uniform convergence of subspace correction methods for some convex optimization problems , 2002, Math. Comput..

[42]  Zi-Cai Li,et al.  Schwarz Alternating Method , 1998 .

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

[44]  J. Borwein,et al.  Two-Point Step Size Gradient Methods , 1988 .

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

[46]  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 .

[47]  H. Schwarz.  Ueber einige Abbildungsaufgaben. , 1869 .