On the alternating direction method of multipliers for nonnegative inverse eigenvalue problems with partial eigendata

We consider the nonnegative inverse eigenvalue problem with partial eigendata, which aims to find a nonnegative matrix such that it is nearest to a pre-estimated nonnegative matrix and satisfies the prescribed eigendata. In this paper, we propose several iterative schemes based on the alternating direction method of multipliers for solving the nonnegative inverse problem. We also extend our schemes to the symmetric case and the cases of prescribed lower bounds and of prescribed entries. Numerical tests (including a practical engineering application in vibrations) show the efficiency of the proposed iterative schemes. (C) 2012 Elsevier B.V. All rights reserved.