7 citations · 19 across the 13 of their papers we have counts for
4 papers · 1 filter
A Nesterov-style Accelerated Gradient Descent Algorithm for the Symmetric Eigenvalue Problem
Foivos Alimisis, Simon Vary, Bart Vandereycken
We develop an accelerated gradient descent algorithm on the Grassmann manifold to compute the subspace spanned by a number of leading eigenvectors of a symmetric positive semi-defi…
Gauss-Southwell type descent methods for low-rank matrix optimization
Guillaume Olikier, André Uschmajew, Bart Vandereycken
We consider gradient-related methods for low-rank matrix optimization with a smooth cost function. The methods operate on single factors of the low-rank factorization and share asp…
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…
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…