A Spectral Gradient Projection Method for the Positive Semi-definite Procrustes Problem

A New Algorithm for the Positive Semi-definite Procrustes Problem

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 lo...

Spectral Projected Gradient Method for the Procrustes Problem

We study and analyze a nonmonotone globally convergent method for minimization on closed sets. This method is based on the ideas from trust-region and Levenberg-Marquardt methods. Thus, the subproblems consists in minimizing a quadratic model of the objective function subject to a given constraint set. We incorporate concepts of bidiagonalization and calculation of the SVD “with inaccuracy” to ...

A note on the complex semi-definite matrix Procrustes problem

This note outlines an algorithm for solving the complex “matrix Procrustes problem”. This is a least-squares approximation over the cone of positive semi-definite Hermitian matrices, which has a number of applications in the areas of Optimization, Signal Processing and Control. The work generalises the method of [J.C. Allwright, “Positive semidefinite matrices: Characterization via conical hull...

A semi-analytical approach for the positive semidefinite Procrustes problem

The positive semidefinite Procrustes (PSDP) problem is the following: given rectangular matrices X and B, find the symmetric positive semidefinite matrix A that minimizes the Frobenius norm of AX − B. No general procedure is known that gives an exact solution. In this paper, we present a semi-analytical approach to solve the PSDP problem. First, we characterize completely the set of optimal sol...

A Regularized Gradient Projection Method for the Minimization Problem