An $\mathcal O(1/{k})$ Convergence Rate for the Variable Stepsize Bregman Operator Splitting Algorithm
From MaRDI portal
Publication:2807288
DOI10.1137/15100401XzbMath1381.49009OpenAlexW2398395170MaRDI QIDQ2807288
Maryam Yashtini, William W. Hager, Hongchao Zhang
Publication date: 20 May 2016
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/15100401x
nonsmooth optimizationconvex optimizationvariational inequalitysaddle point problemergodic convergenceBOSVS
Convex programming (90C25) Numerical optimization and variational techniques (65K10) Variational inequalities (49J40) Numerical methods for variational inequalities and related problems (65K15)
Related Items
Iteration-complexity analysis of a generalized alternating direction method of multipliers, Accelerated Bregman operator splitting with backtracking, Inexact alternating direction methods of multipliers for separable convex optimization, Euler's elastica-based algorithm for parallel MRI reconstruction using sensitivity encoding, Improved Pointwise Iteration-Complexity of A Regularized ADMM and of a Regularized Non-Euclidean HPE Framework, Alternating Direction Method of Multiplier for Euler’s Elastica-Based Denoising, Multi-block nonconvex nonsmooth proximal ADMM: convergence and rates under Kurdyka-Łojasiewicz property, Efficient alternating minimization methods for variational edge-weighted colorization models, Convergence rates for an inexact ADMM applied to separable convex optimization, Pointwise and ergodic convergence rates of a variable metric proximal alternating direction method of multipliers, Scaling Techniques for $\epsilon$-Subgradient Methods, On the iteration-complexity of a non-Euclidean hybrid proximal extragradient framework and of a proximal ADMM, A partially inexact proximal alternating direction method of multipliers and its iteration-complexity analysis, Convergence and rate analysis of a proximal linearized ADMM for nonconvex nonsmooth optimization, On the pointwise iteration-complexity of a dynamic regularized ADMM with over-relaxation stepsize, An inexact ADMM with proximal-indefinite term and larger stepsize
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Nonlinear total variation based noise removal algorithms
- Smooth minimization of non-smooth functions
- Augmented Lagrangian method for total variation restoration with non-quadratic fidelity
- A box constrained gradient projection algorithm for compressed sensing
- Duality-based algorithms for total-variation-regularized image restoration
- A unified primal-dual algorithm framework based on Bregman iteration
- On the weak convergence of an ergodic iteration for the solution of variational inequalities for monotone operators in Hilbert space
- A dual algorithm for the solution of nonlinear variational problems via finite element approximation
- Introductory lectures on convex optimization. A basic course.
- Bregman operator splitting with variable stepsize for total variation image reconstruction
- An alternating direction approximate Newton algorithm for ill-conditioned inverse problems with application to parallel MRI
- On the $O(1/n)$ Convergence Rate of the Douglas–Rachford Alternating Direction Method
- Fast Algorithms for Image Reconstruction with Application to Partially Parallel MR Imaging
- A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science
- NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
- Gradient-Based Methods for Sparse Recovery
- On the Complexity of the Hybrid Proximal Extragradient Method for the Iterates and the Ergodic Mean
- A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
- A New Total Variation Method for Multiplicative Noise Removal
- The Split Bregman Method for L1-Regularized Problems
- A Fast Algorithm for Edge-Preserving Variational Multichannel Image Restoration
- Fixed-Point Continuation for $\ell_1$-Minimization: Methodology and Convergence
- Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction
- Augmented Lagrangian Method, Dual Methods, and Split Bregman Iteration for ROF, Vectorial TV, and High Order Models
- Two-Point Step Size Gradient Methods
- A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
- Sparse Reconstruction by Separable Approximation
- Prox-Method with Rate of Convergence O(1/t) for Variational Inequalities with Lipschitz Continuous Monotone Operators and Smooth Convex-Concave Saddle Point Problems
- Iterative Methods for Total Variation Denoising
- Rate of Convergence Analysis of Decomposition Methods Based on the Proximal Method of Multipliers for Convex Minimization
- Optimal Primal-Dual Methods for a Class of Saddle Point Problems
- Iteration-Complexity of Block-Decomposition Algorithms and the Alternating Direction Method of Multipliers
- Fast Image Recovery Using Variable Splitting and Constrained Optimization
- Partial Regularity for a Selective Smoothing Functional for Image Restoration in BV Space
- Convex Analysis
- Compressed sensing
