Sparse Sylvester Equation Via Alternating Direction Method of Multipliers

Numerous solutions have been investigated or ap-plied for both the Sylvester equation and the sparse Sylvester equation. In this paper, we employ the alternating direction method of multipliers (ADMM) to solve the sparse Sylvester equation, while imposing the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{0}$</tex> norm to the original Sylvester equation formulation. We analyze the iteration scheme for updating each variable and present a corresponding algorithm by extending the classical ADMM. Additionally, several numerical experiments are conducted to validate its feasibility and efficiency.