linearized alternating direction method of multipliers

Inertial primal-dual algorithms for structured convex optimization

Published: 2014/09/10

Convex and Nonsmooth Optimization image reconstruction, inertial primal-dual algorithm, linearized alternating direction method of multipliers, primal-dual algorithms, proximal point algorithm, structured convex optimization, total variation

The primal-dual algorithm recently proposed by Chambolle \& Pock (abbreviated as CPA) for structured convex optimization is very efficient and popular. It was shown by Chambolle \& Pock in \cite{CP11} and also by Shefi \& Teboulle in \cite{ST14} that CPA and variants are closely related to preconditioned versions of the popular alternating direction method of … Read more

A general inertial proximal point method for mixed variational inequality problem

Published: 2014/07/30, Updated: 2014/08/01

Caihua Chen

Shiqian Ma

Junfeng Yang

Convex and Nonsmooth Optimization inertial linearized alternating direction method of multipliers, inertial proximal point method, linearized alternating direction method of multipliers, mixed variational inequality, proximal point algorithm

In this paper, we first propose a general inertial proximal point method for the mixed variational inequality (VI) problem. Based on our knowledge, without stronger assumptions, convergence rate result is not known in the literature for inertial type proximal point methods. Under certain conditions, we are able to establish the global convergence and a $o(1/k)$ … Read more