A partially inexact ADMM with o(1/n) asymptotic convergence rate, 𝒪(1/n) complexity, and immediate relative error tolerance

DOI10.1080/02331934.2020.1772255OpenAlexW3032929167MaRDI QIDQ5860817

Benar Fux Svaiter

Publication date: 23 November 2021

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331934.2020.1772255

zbMATH Keywords

alternating direction method of multipliersrelative error criterioniteration-complexity

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Convex programming (90C25) Abstract computational complexity for mathematical programming problems (90C60) Numerical optimization and variational techniques (65K10) Monotone operators and generalizations (47H05) Decomposition methods (49M27) Error analysis and interval analysis (65G99)

Cites Work

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• A practical relative error criterion for augmented Lagrangians
• An inexact alternating direction method of multipliers with relative error criteria
• On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
• Enlargement of monotone operators with applications to variational inequalities
• Introductory lectures on convex optimization. A basic course.
• A hybrid approximate extragradient-proximal point algorithm using the enlargement of a maximal monotone operator
• Error bounds for proximal point subproblems and associated inexact proximal point algorithms
• An inexact alternating direction method of multipliers for the solution of linear complementarity problems arising from free boundary problems
• Relative-error approximate versions of Douglas-Rachford splitting and special cases of the ADMM
• Approximate ADMM algorithms derived from Lagrangian splitting
• A generalized alternating direction method of multipliers with semi-proximal terms for convex composite conic programming
• On inexact ADMMs with relative error criteria
• Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods
• A partially inexact proximal alternating direction method of multipliers and its iteration-complexity analysis
• Inexact alternating direction methods of multipliers for separable convex optimization
• A family of projective splitting methods for the sum of two maximal monotone operators
• Iteration-complexity analysis of a generalized alternating direction method of multipliers
• An Inexact Hybrid Generalized Proximal Point Algorithm and Some New Results on the Theory of Bregman Functions
• A UNIFIED FRAMEWORK FOR SOME INEXACT PROXIMAL POINT ALGORITHMS^*
• On the $O(1/n)$ Convergence Rate of the Douglas–Rachford Alternating Direction Method
• Improved Pointwise Iteration-Complexity of A Regularized ADMM and of a Regularized Non-Euclidean HPE Framework
• On the Complexity of the Hybrid Proximal Extragradient Method for the Iterates and the Ergodic Mean
• General Projective Splitting Methods for Sums of Maximal Monotone Operators
• Multi-Agent Distributed Optimization via Inexact Consensus ADMM
• Iteration-Complexity of Block-Decomposition Algorithms and the Alternating Direction Method of Multipliers
• A family of enlargements of maximal monotone operators