A Two-phase Augmented Lagrangian Method For H-weighted Nearest Correlation Matrix Problem

H-weighted nearest correlation matrix(HNCM)problem has a wide application in the financial industry,but there are few efficient methods for H-weighted nearest correlation matrix problem in the literature.The main reason is that an analytic formula for the metric projection onto the positive semidefinite matrix cone under the H-weight is not available.It's well known that the augmented Lagrangian method has the fast local convergence,and the alternating direction multiplier method(ADMM)can quickly obtain an approximate optimal solution with a low accuracy.Based on the above observation,we introduce a two-phase method that combining with the advantages of both methods.At Phase ?,we use Gauss-Seidel ADMM to obtain a reasonably good initial point,and at Phase ? use the augmented Lagrangian method to obtain high accurate solutions.The numerical results show the method is effective.