Improved Pointwise Iteration-Complexity of A Regularized ADMM and of a Regularized Non-Euclidean HPE Framework

DOI10.1137/16M1055530MaRDI QIDQ2968178

Renato D. C. Monteiro, Jefferson G. Melo, Max L. N. Gonçalves

Publication date: 10 March 2017

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.01140

zbMATH Keywords

regularizationconvex programalternating direction method of multipliershybrid proximal extragradient methodfirst-order methodsinexact proximal point methodpointwise iteration-complexitynon-Euclidean Bregman distances

Mathematics Subject Classification ID

Convex programming (90C25) Abstract computational complexity for mathematical programming problems (90C60) Nonlinear programming (90C30) Numerical optimization and variational techniques (65K10) Monotone operators and generalizations (47H05) Decomposition methods (49M27) Variational and other types of inclusions (47J22)

Related Items

A survey on some recent developments of alternating direction method of multipliers, Iteration-complexity analysis of a generalized alternating direction method of multipliers, An inexact Spingarn's partial inverse method with applications to operator splitting and composite optimization, A simple alternating direction method for the conic trust region subproblem, Tikhonov-like methods with inexact minimization for solving linear ill-posed problems, Cauchy noise removal by nonconvex ADMM with convergence guarantees, Complexity of the relaxed Peaceman-Rachford splitting method for the sum of two maximal strongly monotone operators, Pointwise and ergodic convergence rates of a variable metric proximal alternating direction method of multipliers, 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, Iteration complexity of an inexact Douglas-Rachford method and of a Douglas-Rachford-Tseng's F-B four-operator splitting method for solving monotone inclusions, On the pointwise iteration-complexity of a dynamic regularized ADMM with over-relaxation stepsize, A partially inexact ADMM with o(1/n) asymptotic convergence rate, 𝒪(1/n) complexity, and immediate relative error tolerance

Uses Software

• GADMM

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
• On the convergence properties of a majorized alternating direction method of multipliers for linearly constrained convex optimization problems with coupled objective functions
• A dual algorithm for the solution of nonlinear variational problems via finite element approximation
• Enlargement of monotone operators with applications to variational inequalities
• A hybrid approximate extragradient-proximal point algorithm using the enlargement of a maximal monotone operator
• Global convergence of ADMM in nonconvex nonsmooth optimization
• A simple algorithm for a class of nonsmooth convex-concave saddle-point problems
• A first-order primal-dual algorithm for convex problems with applications to imaging
• On non-ergodic convergence rate of Douglas-Rachford alternating direction method of multipliers
• Generalized alternating direction method of multipliers: new theoretical insights and applications
• On the maximal monotonicity of subdifferential mappings
• An Inexact Hybrid Generalized Proximal Point Algorithm and Some New Results on the Theory of Bregman Functions
• An $\mathcal O(1/{k})$ Convergence Rate for the Variable Stepsize Bregman Operator Splitting Algorithm
• Hankel Matrix Rank Minimization with Applications to System Identification and Realization
• On the $O(1/n)$ Convergence Rate of the Douglas–Rachford Alternating Direction Method
• On the Complexity of the Hybrid Proximal Extragradient Method for the Iterates and the Ergodic Mean
• A Monotone+Skew Splitting Model for Composite Monotone Inclusions in Duality
• Complexity of Variants of Tseng's Modified F-B Splitting and Korpelevich's Methods for Hemivariational Inequalities with Applications to Saddle-point and Convex Optimization Problems
• Accelerating Block-Decomposition First-Order Methods for Solving Composite Saddle-Point and Two-Player Nash Equilibrium Problems
• An Accelerated HPE-Type Algorithm for a Class of Composite Convex-Concave Saddle-Point Problems
• Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction
• Variational Analysis
• An accelerated non-Euclidean hybrid proximal extragradient-type algorithm for convex–concave saddle-point problems
• A primal–dual fixed point algorithm for convex separable minimization with applications to image restoration
• Fast Alternating Direction Optimization Methods
• Solving Coupled Composite Monotone Inclusions by Successive Fejér Approximations of their Kuhn--Tucker Set
• An Accelerated Linearized Alternating Direction Method of Multipliers
• Iteration-Complexity of Block-Decomposition Algorithms and the Alternating Direction Method of Multipliers
• Local Linear Convergence of the Alternating Direction Method of Multipliers on Quadratic or Linear Programs
• Regularized HPE-Type Methods for Solving Monotone Inclusions with Improved Pointwise Iteration-Complexity Bounds
• Convex Analysis