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

Min Li and Zhongming Wu ()
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Min Li: School of Management and Engineering, Nanjing University, Nanjing 210093, P. R. China
Zhongming Wu: School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2021, vol. 38, issue 01, 1-34

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 (0, (1 + 5)/2). Under more general conditions, we establish the global convergence and Q-linear convergence rate of the proposed methods.

Keywords: Convex composite optimization; indefinite proximal terms; inexact; majorized ADMM; relative error control; symmetric Gauss–Seidel (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0217595920500359

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