Alternating Direction Method for a Class of Sylvester Matrix Equations with Linear Matrix Inequality Constraint

摘要

This paper introduces an alternating direction method of multi pliers (ADMM) for finding solutions to a class of Sylvester matrix equation AXB = E subject to a linear matrix inequality constraint CXD = G. Preliminary convergence properties of ADMM are presented. Numerical experiments are performed to illustrate the feasibility and effectiveness of ADMM. In addition, some numerical comparisons with a recent algorithm are also given.