A family of accelerated inexact augmented Lagrangian methods with applications to image restoration

In this paper, we focus on a class of convex optimization problems subject to equality or inequality constraints and have developed an Accelerated Inexact Augmented Lagrangian Method (AI-ALM). Different relative error criteria are designed to solve the subproblem of AI-ALM inexactly, and the popular used relaxation step is exploited to accelerate the convergence. By a … Read more

An inexact ADMM with proximal-indefinite term and larger stepsize

This work is devoted to developing an inexact ADMM for solving a family of multi-block separable convex optimization problems subject to linear equality constraints, where the problem variables are artificially partitioned into two groups. The first grouped subproblems are solved inexactly and and parallelly under relative error criterions, while the second grouped single subproblem (often … Read more

Iteration complexity analysis of a partial LQP-based alternating direction method of multipliers

In this paper, we consider a prototypical convex optimization problem with multi-block variables and separable structures. By adding the Logarithmic Quadratic Proximal (LQP) regularizer with suitable proximal parameter to each of the first grouped subproblems, we develop a partial LQP-based Alternating Direction Method of Multipliers (ADMM-LQP). The dual variable is updated twice with relatively larger … Read more