A three-block linearized generalized ADMM based iterative algorithm for separable convex programming with application to an image compression problem

Abstract

The generalized alternating direction method of multipliers (GADMM) has attracted considerable attention due to its versatile applications. This study introduces an innovative adaptation called the linearized GADMM (L-GADMM), which is specifically tailored for solving convex optimization problems. The objective function of the problems under consideration encompasses three distinct convex components with no interdependencies among variables or linear constraints. We establish a set of sufficient conditions ensuring the global convergence of the proposed L-GADMM technique for the three-block separable convex minimization problem. Moreover, a series of numerical experiments are conducted to showcase the effectiveness of L-GADMM in tasks such as image compression and calibration of correlation matrices. © 2025 Elsevier B.V.