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 Steighaugs 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.
Original language | English |
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Pages (from-to) | 327-349 |
Number of pages | 23 |
Journal | Computational Optimization and Applications |
Volume | 50 |
Issue number | 2 |
DOIs | |
Publication status | Published - Oct 2011 |
Externally published | Yes |
Keywords
- Block relaxation methods
- Correlation matrix
- Factor structure
- Majorization methods