A New Algorithm for the Positive Semi-definite Procrustes Problem
نویسنده
چکیده
For arbitrary real matrices F and G, the positive semi-deenite Procrustes problem is minimization of the Frr obenius norm of F ? PG with respect to positive semi-deenite symmetric P. Existing solution algorithms are based on a convex programming approach. Here an unconstrained non-convex approach is taken, namely writing P = E 0 E and optimizing with respect to E. The main result is that all local minimizers are in fact global. A modiied 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.
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