A new algorithm for the positive semi-definite Procrustes problem

For arbitrary real matrices F and G, the positive semi-definite Procrustes problem is minimization of the Frobenius norm of F-PG with respect to positive semi-definite symmetric P. Existing solution algorithms are based on a convex programming approach. Here an unconstrained nonconvex approach is taken, namely writing P=E´E and optimizing with respect to E. The main result is that all local minimizers are in fact global. A modified Newton algorithm is proposed which, when used to solve a test example that has appeared in the literature, exhibits substantially superior convergence to a minimizer