Block relaxation and majorization methods for the nearest correlation matrix with factor structure

Authors:
Qingna Li;Houduo Qi;Naihua Xiu
Affiliations:
Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, China 100080;School of Mathematics, University of Southampton, Highfield, UK SO17 1BJ;Department of Mathematics, Beijing Jiaotong University, Beijing, China 100044
Venue:
Computational Optimization and Applications
Year:
2011

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Abstract

We propose two numerical methods, namely the alternating block relaxation method and the alternating majorization method, for the problem of nearest correlation matrix with factor structure, which is highly nonconvex. In the block relaxation method, the subproblem is of the standard trust region problem, which is solved by Steighaug's truncated conjugate gradient method or by the exact trust region method. In the majorization method, the subproblem has a closed-form solution. We then apply the majorization method to the case where nonnegative factors are required. The numerical results confirm that the proposed methods work quite well and are competitive against the best available methods.