On the Convergence Rate of Inexact Majorized sGS ADMM with Indefinite Proximal Terms for Convex Composite Programming-Reference-Cited by-同舟云学术

On the Convergence Rate of Inexact Majorized sGS ADMM with Indefinite Proximal Terms for Convex Composite Programming

Published:2020-10-01 Issue:01 Volume:38 Page:2050035
ISSN:0217-5959
Container-title:Asia-Pacific Journal of Operational Research
language:en
Short-container-title:Asia Pac. J. Oper. Res.

Author:

Li Min¹,Wu Zhongming²

Affiliation:

1. School of Management and Engineering, Nanjing University, Nanjing 210093, P. R. China

2. School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China

Abstract

In this paper, we propose an inexact majorized symmetric Gauss–Seidel (sGS) alternating direction method of multipliers (ADMM) with indefinite proximal terms for multi-block convex composite programming. This method is a specific form of the inexact majorized ADMM which is further proposed to solve a general two-block separable optimization problem. The new methods adopt certain relative error criteria to solve the involving subproblems approximately, and the step-sizes allow to choose in the scope [Formula: see text]. Under more general conditions, we establish the global convergence and Q-linear convergence rate of the proposed methods.

Publisher

World Scientific Pub Co Pte Lt

Subject

Management Science and Operations Research,Management Science and Operations Research

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0217595920500359

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