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math.OC2022★ 2 cited
Geodesic Convexity of the Symmetric Eigenvalue Problem and Convergence of Riemannian Steepest Descent
Foivos Alimisis, Bart Vandereycken
We study the convergence of the Riemannian steepest descent algorithm on the Grassmann manifold for minimizing the block version of the Rayleigh quotient of a symmetric matrix. Eve…
math.OC2022★ 3 cited
Riemannian optimization using three different metrics for Hermitian PSD fixed-rank constraints: an extended version
Shixin Zheng, Wen Huang, Bart Vandereycken +1
For smooth optimization problems with a Hermitian positive semi-definite fixed-rank constraint, we consider three existing approaches including the simple Burer--Monteiro method, a…