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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 598563, 10 pages
http://dx.doi.org/10.1155/2014/598563
Research Article

Proximal Alternating Direction Method with Relaxed Proximal Parameters for the Least Squares Covariance Adjustment Problem

1School of Mathematics and Physics, Changzhou University, Jiangsu 213164, China
2College of Science, Nanjing University of Posts and Telecommunications, Jiangsu 210003, China

Received 13 June 2013; Accepted 27 July 2013; Published 21 January 2014

Academic Editor: Abdellah Bnouhachem

Copyright © 2014 Minghua Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the problem of seeking a symmetric positive semidefinite matrix in a closed convex set to approximate a given matrix. This problem may arise in several areas of numerical linear algebra or come from finance industry or statistics and thus has many applications. For solving this class of matrix optimization problems, many methods have been proposed in the literature. The proximal alternating direction method is one of those methods which can be easily applied to solve these matrix optimization problems. Generally, the proximal parameters of the proximal alternating direction method are greater than zero. In this paper, we conclude that the restriction on the proximal parameters can be relaxed for solving this kind of matrix optimization problems. Numerical experiments also show that the proximal alternating direction method with the relaxed proximal parameters is convergent and generally has a better performance than the classical proximal alternating direction method.