ADMM-Based Methods for Nearness Skew-Symmetric and Symmetric Solutions of Matrix Equation $AXB = C$

Abstract

New equivalent forms of a matrix nearness problem are proposed and necessary and sufficient conditions for a skew-symmetric or symmetric matrix $X$^∗ to be a solution of the problem are obtained. In order to find approximate solutions of the problem, we employ two ADMM-based iterative methods and prove their global convergence. Numerical simulations demonstrate the effectiveness of the methods developed.