Inertial, Corrected, Primal-Dual Proximal Splitting

We study inertial versions of primal-dual proximal splitting, also known as the Chambolle--Pock method. Our starting point is the preconditioned proximal point formulation of this method. By adding...

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

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

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

[4]  A. Chambolle,et al.  On the convergence of the iterates of "FISTA" , 2015 .

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

[6]  T. Pock,et al.  Second order total generalized variation (TGV) for MRI , 2011, Magnetic resonance in medicine.

[7]  Shiqian Ma,et al.  Inertial primal-dual algorithms for structured convex optimization , 2014, 1409.2992.

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

[9]  Alberto Bemporad,et al.  Douglas-rachford splitting: Complexity estimates and accelerated variants , 2014, 53rd IEEE Conference on Decision and Control.

[10]  Kristian Bredies,et al.  Accelerated Douglas-Rachford methods for the solution of convex-concave saddle-point problems , 2016, 1604.06282.

[11]  Samuli Siltanen,et al.  Linear and Nonlinear Inverse Problems with Practical Applications , 2012, Computational science and engineering.

[12]  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.

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

[14]  Hédy Attouch,et al.  Convergence Rates of Inertial Forward-Backward Algorithms , 2018, SIAM J. Optim..

[15]  Carola-Bibiane Schönlieb,et al.  Bilevel Parameter Learning for Higher-Order Total Variation Regularisation Models , 2015, Journal of Mathematical Imaging and Vision.

[16]  Tuomo Valkonen,et al.  Block-proximal methods with spatially adapted acceleration , 2016, ETNA - Electronic Transactions on Numerical Analysis.

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

[18]  Jeffrey A. Fessler,et al.  Another Look at the Fast Iterative Shrinkage/Thresholding Algorithm (FISTA) , 2016, SIAM J. Optim..

[19]  H. Attouch,et al.  An Inertial Proximal Method for Maximal Monotone Operators via Discretization of a Nonlinear Oscillator with Damping , 2001 .

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

[21]  ANTONIN CHAMBOLLE,et al.  An Algorithm for Total Variation Minimization and Applications , 2004, Journal of Mathematical Imaging and Vision.

[22]  Carola-Bibiane Schönlieb,et al.  Preconditioned ADMM with Nonlinear Operator Constraint , 2015, System Modelling and Optimization.

[23]  Thomas Pock,et al.  Acceleration of the PDHGM on strongly convex subspaces , 2015, ArXiv.

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

[25]  Kristian Bredies,et al.  Preconditioned Douglas–Rachford Algorithms for TV- and TGV-Regularized Variational Imaging Problems , 2015, Journal of Mathematical Imaging and Vision.

[26]  Tuomo Valkonen,et al.  Testing and Non-linear Preconditioning of the Proximal Point Method , 2017, Applied Mathematics & Optimization.