Riemannian linearized proximal algorithms for nonnegative inverse eigenvalue problem

We study the issue of numerically solving the nonnegative inverse eigenvalue problem (NIEP). At first, we reformulate the NIEP as a convex composite optimization problem on Riemannian manifolds. Then we develop a scheme of the Riemannian linearized proximal algorithm (R-LPA) to solve the NIEP. Under some mild conditions, the local and global convergence results of the R-LPA for the NIEP are established, respectively. Moreover, numerical experiments are presented. Compared with the Riemannian Newton-CG method in Z. Zhao et al. (Numer. Math. 140:827-855, 2018), this R-LPA owns better numerical performances for large scale problems and sparse matrix cases, which is due to the smaller dimension of the Riemannian manifold derived from the problem formulation of the NIEP as a convex composite optimization problem.