An Alternating Direction Method For H-weighted Nearest Correlation Matrix Problem

The nearest correlation matrix problem is to find a correlation matrix which is closest to a given symmetric matrix in the Frobenius norm. There are many methods have been developed for computing the nearest correlation matrix problem, but there are fewer methods for solving it under the H-weight. The main reason is that it is difficulty to obtain a computable formula for the projection of X ∈ Sn onto the closed convex cone Sn+ under the H-weight. In this paper, we introduce the alternating direction method that can avoid the computation of the metric projection under the H-weight. We compare the alternating direction method approach with the existing approach numerically and show the efficiency of the alternating direction method for solving the H-weighted nearest correlation matrix.