Alternating direction method for a class of constrained matrix approximation problems

In this paper, we consider the matrix approximation problems under spectral norm, with linear and positive semidefinite constraints. The difficulty in solving such problems lies in the presence of the spectral norm and the positive semidefinite constraint. Based on the recent progress in matrix optimization problems, especially in the Moreau-Yosida regularization of the spectral norm function, we axe now equipped with more tools to handle the spectral norm. We apply the alternating direction method to solve it. Extensive numerical results for the fastest distributed linear averaging problem and the nearest correlation matrix problem are presented to confirm the efficiency of the proposed method.