Convex constrained optimization for large‐scale generalized Sylvester equations

We propose and study the use of convex constrained optimization techniques for solving large‐scale Generalized Sylvester Equations (GSE). For that, we adapt recently developed globalized variants of the projected gradient method to a convex constrained least‐squares approach for solving GSE. We demonstrate the effectiveness of our approach on two different applications. First, we apply it to solve the GSE that appears after applying left and right preconditioning schemes to the linear problems associated with the discretization of some partial differential equations. Second, we apply the new approach, combined with a Tikhonov regularization term, to restore some blurred and highly noisy images.