Convergence Analysis of an Inexact Three-Operator Splitting Algorithm

[1]  M. Solodov,et al.  A UNIFIED FRAMEWORK FOR SOME INEXACT PROXIMAL POINT ALGORITHMS , 2001 .

[2]  Paul Tseng,et al.  A Modified Forward-backward Splitting Method for Maximal Monotone Mappings 1 , 1998 .

[3]  Dirk A. Lorenz,et al.  An Inertial Forward-Backward Algorithm for Monotone Inclusions , 2014, Journal of Mathematical Imaging and Vision.

[4]  Marin Marin,et al.  The theory of generalized thermoelasticity with fractional order strain for dipolar materials with double porosity , 2018, Journal of Materials Science.

[5]  Loic Landrieu,et al.  Preconditioning of a Generalized Forward-Backward Splitting and Application to Optimization on Graphs , 2015, SIAM J. Imaging Sci..

[6]  Marin Marin,et al.  Weak Solutions in Elasticity of Dipolar Porous Materials , 2008 .

[7]  Marc Teboulle,et al.  Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems , 2009, IEEE Transactions on Image Processing.

[8]  Panagiotis Patrinos,et al.  Asymmetric forward–backward–adjoint splitting for solving monotone inclusions involving three operators , 2016, Comput. Optim. Appl..

[9]  J.-C. Pesquet,et al.  A Douglas–Rachford Splitting Approach to Nonsmooth Convex Variational Signal Recovery , 2007, IEEE Journal of Selected Topics in Signal Processing.

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

[11]  Bingsheng He,et al.  An Accelerated Inexact Proximal Point Algorithm for Convex Minimization , 2012, J. Optim. Theory Appl..

[12]  Nikos Komodakis,et al.  Playing with Duality: An overview of recent primal?dual approaches for solving large-scale optimization problems , 2014, IEEE Signal Process. Mag..

[13]  E. Sidky,et al.  Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle–Pock algorithm , 2011, Physics in medicine and biology.

[14]  Pablo A. Lotito,et al.  A Class of Inexact Variable Metric Proximal Point Algorithms , 2008, SIAM J. Optim..

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

[16]  Benar Fux Svaiter,et al.  An Inexact Hybrid Generalized Proximal Point Algorithm and Some New Results on the Theory of Bregman Functions , 2000, Math. Oper. Res..

[17]  Émilie Chouzenoux,et al.  Variable Metric Forward–Backward Algorithm for Minimizing the Sum of a Differentiable Function and a Convex Function , 2013, Journal of Optimization Theory and Applications.

[18]  Bang Công Vu,et al.  A splitting algorithm for dual monotone inclusions involving cocoercive operators , 2011, Advances in Computational Mathematics.

[19]  Xiangyu Wang,et al.  An Inexact Dual Fast Gradient-Projection Method for Separable Convex Optimization with Linear Coupled Constraints , 2016, J. Optim. Theory Appl..

[20]  A. Goldstein.  Convex programming in Hilbert space , 1964 .

[21]  R. Rockafellar.  Monotone Operators and the Proximal Point Algorithm , 1976 .

[22]  I. Loris,et al.  On a generalization of the iterative soft-thresholding algorithm for the case of non-separable penalty , 2011, 1104.1087.

[23]  Laurent Condat,et al.  A Primal–Dual Splitting Method for Convex Optimization Involving Lipschitzian, Proximable and Linear Composite Terms , 2012, Journal of Optimization Theory and Applications.

[24]  Luca Baldassarre,et al.  Accelerated and Inexact Forward-Backward Algorithms , 2013, SIAM J. Optim..

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

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

[27]  Alvaro R. De Pierro,et al.  A new convergence analysis and perturbation resilience of some accelerated proximal forward–backward algorithms with errors , 2015, ArXiv.

[28]  P. L. Combettes,et al.  Solving monotone inclusions via compositions of nonexpansive averaged operators , 2004 .

[29]  Jigen Peng,et al.  A modified primal-dual method with applications to some sparse recovery problems , 2018, Appl. Math. Comput..

[30]  Deren Han,et al.  Inexact Operator Splitting Methods with Selfadaptive Strategy for Variational Inequality Problems , 2007 .

[31]  Mohamed-Jalal Fadili,et al.  A Generalized Forward-Backward Splitting , 2011, SIAM J. Imaging Sci..

[32]  Wang Yao,et al.  Relative-error approximate versions of Douglas–Rachford splitting and special cases of the ADMM , 2018, Math. Program..

[33]  Patrick L. Combettes,et al.  Signal Recovery by Proximal Forward-Backward Splitting , 2005, Multiscale Model. Simul..

[34]  L. Briceño-Arias.  Forward-Douglas–Rachford splitting and forward-partial inverse method for solving monotone inclusions , 2012, 1212.5942.

[35]  C. Byrne,et al.  A unified treatment of some iterative algorithms in signal processing and image reconstruction , 2003 .

[36]  P. L. Combettes,et al.  Variable metric forward–backward splitting with applications to monotone inclusions in duality , 2012, 1206.6791.

[37]  Alfredo N. Iusem,et al.  Inexact Variants of the Proximal Point Algorithm without Monotonicity , 2002, SIAM J. Optim..

[38]  Damek Davis,et al.  A Three-Operator Splitting Scheme and its Optimization Applications , 2015, 1504.01032.

[39]  Myungjoo Kang,et al.  Inexact accelerated augmented Lagrangian methods , 2015, Comput. Optim. Appl..

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

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

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

[43]  Xiaoqun Zhang,et al.  A primal–dual fixed point algorithm for convex separable minimization with applications to image restoration , 2013 .