An inexact alternating direction method of multipliers with relative error criteria

DOI10.1007/s11590-016-1021-9zbMath1367.90089OpenAlexW2295956514MaRDI QIDQ519776

Jiaxin Xie, Xiaobo Yang, An-Ping Liao

Publication date: 5 April 2017

Published in: Optimization Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11590-016-1021-9

zbMATH Keywords

alternating direction method of multipliers (ADMM)sparse signal recoveryinexactnessrelative error criteria

Mathematics Subject Classification ID

Convex programming (90C25)

Related Items (12)

Fast and stable nonconvex constrained distributed optimization: the ELLADA algorithm ⋮ Approximate ADMM algorithms derived from Lagrangian splitting ⋮ A partially inexact generalized primal-dual hybrid gradient method for saddle point problems with bilinear couplings ⋮ An inexact proximal generalized alternating direction method of multipliers ⋮ Approximate customized proximal point algorithms for separable convex optimization ⋮ Inexact generalized ADMM with relative error criteria for linearly constrained convex optimization problems ⋮ On inexact ADMMs with relative error criteria ⋮ A partially inexact proximal alternating direction method of multipliers and its iteration-complexity analysis ⋮ An inexact symmetric ADMM algorithm with indefinite proximal term for sparse signal recovery and image restoration problems ⋮ Approximate first-order primal-dual algorithms for saddle point problems ⋮ A partially inexact ADMM with o(1/n) asymptotic convergence rate, 𝒪(1/n) complexity, and immediate relative error tolerance ⋮ An inexact ADMM with proximal-indefinite term and larger stepsize

Cites Work

• Unnamed Item
• Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
• A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
• A practical relative error criterion for augmented Lagrangians
• On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
• A dual algorithm for the solution of nonlinear variational problems via finite element approximation
• A hybrid approximate extragradient-proximal point algorithm using the enlargement of a maximal monotone operator
• Multiplier and gradient methods
• An Inexact Hybrid Generalized Proximal Point Algorithm and Some New Results on the Theory of Bregman Functions
• Constrained Total Variation Deblurring Models and Fast Algorithms Based on Alternating Direction Method of Multipliers
• Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming
• An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
• On Alternating Direction Methods of Multipliers: A Historical Perspective
• Restoration of Poissonian Images Using Alternating Direction Optimization
• Local Linear Convergence of the Alternating Direction Method of Multipliers on Quadratic or Linear Programs
• Compressed sensing

This page was built for publication: An inexact alternating direction method of multipliers with relative error criteria