The orthogonal Procrustes problem satisfies weak-quasi-strong-convexity, yielding linear convergence of Riemannian gradient descent for invertible matrices and O(1/t) function-value convergence for singular ones.
Error bounds, q uadratic growth, and linear convergence of proximal methods
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A geodesic convexity-like structure for the polar decomposition of a square matrix
The orthogonal Procrustes problem satisfies weak-quasi-strong-convexity, yielding linear convergence of Riemannian gradient descent for invertible matrices and O(1/t) function-value convergence for singular ones.