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

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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.

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Authors and Affiliations

  1. Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100080, China

    Qingna Li

  2. School of Mathematics, University of Southampton, Highfield, Southampton, SO17 1BJ, UK

    Houduo Qi

  3. Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, China

    Naihua Xiu

Authors
  1. Qingna Li
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  2. Houduo Qi
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  3. Naihua Xiu
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Corresponding author

Correspondence to Houduo Qi.

Additional information

Dedicated to Professor Liqun Qi on the occasion of his 65th birthday.

The work of N. Xiu was supported by the National Basic Research Program of China (2010CB732501).

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Li, Q., Qi, H. & Xiu, N. Block relaxation and majorization methods for the nearest correlation matrix with factor structure. Comput Optim Appl 50, 327–349 (2011). https://doi.org/10.1007/s10589-010-9374-y

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