Conditions for Optimal Solutions of Unbalanced Procrustes Problem on Stiefel Manifold (Journal of Computational Mathematics, 2021)
We consider the unbalanced Procrustes problem with an orthonormal constraint on solutions: given matrices $A\in \mathcal{R}^{n× n}$ and $B\in \mathcal{R}^{n× k}$, $n>k$, minimize the residual $\|AQ-B\|_F$ over the Stiefel manifold of orthonormal matrices. Theoretical analysis on necessary conditions and sufficient conditions for optimal solutions of the unbalanced Procrustes problem is given.
Keywords: Procrustes problem; Stiefel manifold; Necessary condition; Sufficient condition.