A Bregman-style Partially Symmetric Alternating Direction Method of Multipliers for Nonconvex Multi-block Optimization

[1]  Miantao Chao,et al.  An inertial Bregman generalized alternating direction method of multipliers for nonconvex optimization , 2021, Journal of Applied Mathematics and Computing.

[2]  Yongzhong Song,et al.  An extended proximal ADMM algorithm for three-block nonconvex optimization problems , 2021, J. Comput. Appl. Math..

[3]  Chun Zhang,et al.  A Linearized Alternating Direction Method of Multipliers for a Special Three-Block Nonconvex Optimization Problem of Background/Foreground Extraction , 2020, IEEE Access.

[4]  Kresimir Mihic,et al.  On a Randomized Multi-Block ADMM for Solving Selected Machine Learning Problems , 2019, ArXiv.

[5]  Zongben Xu,et al.  Convergence of multi-block Bregman ADMM for nonconvex composite problems , 2015, Science China Information Sciences.

[6]  Deren Han,et al.  Convergence of ADMM for multi-block nonconvex separable optimization models , 2017 .

[7]  Xiaojun Chen,et al.  Alternating Direction Method of Multipliers for a Class of Nonconvex and Nonsmooth Problems with Applications to Background/Foreground Extraction , 2015, SIAM J. Imaging Sci..

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

[9]  Guoyin Li,et al.  Global Convergence of Splitting Methods for Nonconvex Composite Optimization , 2014, SIAM J. Optim..

[10]  Hong-Kun Xu,et al.  Convergence of Bregman alternating direction method with multipliers for nonconvex composite problems , 2014, 1410.8625.

[11]  Marc Teboulle,et al.  Proximal alternating linearized minimization for nonconvex and nonsmooth problems , 2013, Mathematical Programming.

[12]  Arindam Banerjee,et al.  Bregman Alternating Direction Method of Multipliers , 2013, NIPS.

[13]  Zongben Xu,et al.  Accelerated L1/2 regularization based SAR imaging via BCR and reduced Newton skills , 2013, Signal Process..

[14]  Xiaoming Yuan,et al.  Linearized alternating direction method of multipliers with Gaussian back substitution for separable convex programming , 2013 .

[15]  Yiwen Ju,et al.  Structure and coalbed methane occurrence in tectonically deformed coals , 2012, Science China Earth Sciences.

[16]  Zongben Xu,et al.  Sparse SAR imaging based on L1/2 regularization , 2012, Science China Information Sciences.

[17]  Zongben Xu,et al.  $L_{1/2}$ Regularization: A Thresholding Representation Theory and a Fast Solver , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[18]  Bingsheng He,et al.  Linearized Alternating Direction Method with Gaussian Back Substitution for Separable Convex Programming , 2011 .

[19]  Xiaoming Yuan,et al.  A Note on the Alternating Direction Method of Multipliers , 2012, J. Optim. Theory Appl..

[20]  Yi Ma,et al.  Robust principal component analysis? , 2009, JACM.

[21]  Shiqian Ma,et al.  Sparse Inverse Covariance Selection via Alternating Linearization Methods , 2010, NIPS.

[22]  Hédy Attouch,et al.  Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Lojasiewicz Inequality , 2008, Math. Oper. Res..

[23]  Hédy Attouch,et al.  On the convergence of the proximal algorithm for nonsmooth functions involving analytic features , 2008, Math. Program..

[24]  Yurii Nesterov,et al.  Introductory Lectures on Convex Optimization - A Basic Course , 2014, Applied Optimization.

[25]  D. Gabay.  Applications of the method of multipliers to variational inequalities , 1983 .

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

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

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

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

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