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

We propose two numerical methods, namely the block relaxation and 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 trust region method of [21]. In the majorization method, the subproblem has a closed-form solution. We then extend the majorization method to the case where nonnegative factors are required. The numerical results confirm that the proposed methods worked quite well and are competitive against the best available methods.