An iterative method based on ADMM for solving generalized Sylvester matrix equations

As is well known, the alternating direction method of multipliers (ADMM) is one of the most famous distributed algorithms for solving the convex optimization problems. In this paper, by applying the hierarchical identification principle, we propose an iterative algorithm based on matrix form of ADMM for finding the least squares solution of the generalized Sylvester matrix equation AX B + CX D = E. We prove that the proposed method is convergent under some common conditions for any initial matrices. The simplicity and effectiveness of the new method are shown by the reported numerical results. (c) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.