Scaled form Alternating Direction Method of Multipliers and its variants for solving the matrix equation AXB+CXD=E

The generalized Sylvester matrix equation is solved using the scaled ADMM in a composite optimization approach in this paper. The theoretical analysis provides optimality conditions and stopping criteria for the proposed algorithm. The proposed method is globally convergent, according to the convergence study. Furthermore, this paper offers dynamic parameters and relaxation techniques to improve the scaled ADMM's convergence performance. Numerical experiments validate the algorithm's effectiveness.