2 citations · 2 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 Mlinarić, 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…
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…
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…
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…
Retractions on closed sets
Guillaume Olikier
On a manifold or a closed subset of a Euclidean vector space, a retraction enables to move in the direction of a tangent vector while staying on the set. Retractions are a versatil…
Rank Estimation for Third-Order Tensor Completion in the Tensor-Train Format
Charlotte Vermeylen, Guillaume Olikier, P. -A. Absil +1
We propose a numerical method to obtain an adequate value for the upper bound on the rank for the tensor completion problem on the variety of third-order tensors of bounded tensor-…