4 papers
Graph-Regularized Low-Rank Matrix Completion by Variable Projection
Benoît Loucheur, P. -A. Absil, Michel Journée
We address the low-rank matrix completion problem by incorporating graph regularization into the existing Riemannian Trust-Region Matrix Completion (RTRMC) framework. The latter us…
A second-order method landing on the Stiefel manifold via Newton$\unicode{x2013}$Schulz iteration
Xinhui Xiong, Bin Gao, P. -A. Absil
Retraction-free approaches offer attractive low-cost alternatives to Riemannian methods on the Stiefel manifold, but they are often first-order, which may limit the efficiency unde…
The tangent cone to the real determinantal variety: various expressions and a proof
Guillaume Olikier, Petar MlinariÄ, P. -A. Absil +1
The set of real matrices of upper-bounded rank is a real algebraic variety called the real generic determinantal variety. An explicit description of the tangent cone to that variet…
Low-rank optimization methods based on projected projected-gradient descent that accumulate at Bouligand stationary points
Guillaume Olikier, Kyle A. Gallivan, P. -A. Absil
This paper considers the problem of minimizing a differentiable function with locally Lipschitz continuous gradient on the algebraic variety of real matrices of upper-bounded rank.…