3 citations · 3 across the 2 of their papers we have counts for
7 papers
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.…
Eigengap Sparsity for Covariance Parsimony
Tom Szwagier, Guillaume Olikier, Xavier Pennec
Covariance estimation is a central problem in statistics. An important issue is that there are rarely enough samples to accurately estimate the coefficients in di…
Projected gradient descent accumulates at Bouligand stationary points
Guillaume Olikier, Irène Waldspurger
This paper considers the projected gradient descent (PGD) algorithm for the problem of minimizing a continuously differentiable function on a nonempty closed subset of a Euclidean…
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…
Computing Bouligand stationary points efficiently in low-rank optimization
Guillaume Olikier, P. -A. Absil
This paper considers the problem of minimizing a differentiable function with locally Lipschitz continuous gradient on the algebraic variety of all -by- real matrices of rank…