8 citations · 29 across the 13 of their papers we have counts for
13 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-…
An Approximate Projection onto the Tangent Cone to the Variety of Third-Order Tensors of Bounded Tensor-Train Rank
Charlotte Vermeylen, Guillaume Olikier, Marc Van Barel
An approximate projection onto the tangent cone to the variety of third-order tensors of bounded tensor-train rank is proposed and proven to satisfy a better angle condition than t…
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…
First-order optimization on stratified sets
Guillaume Olikier, Kyle A. Gallivan, P. -A. Absil
We consider the problem of minimizing a differentiable function with locally Lipschitz continuous gradient on a stratified set and present a first-order algorithm designed to find…
An apocalypse-free first-order low-rank optimization algorithm with at most one rank reduction attempt per iteration
Guillaume Olikier, P. -A. Absil
We consider the problem of minimizing a differentiable function with locally Lipschitz continuous gradient over the real determinantal variety, and present a first-order algorithm…
Comparison of an Apocalypse-Free and an Apocalypse-Prone First-Order Low-Rank Optimization Algorithm
Guillaume Olikier, Kyle A. Gallivan, P. -A. Absil
We compare two first-order low-rank optimization algorithms, namely (Schneider and Uschmajew, 2015), which has been proven to be apocalypse-prone (Levin et al…
On the continuity of the tangent cone to the determinantal variety
Guillaume Olikier, P. -A. Absil
Tangent and normal cones play an important role in constrained optimization to describe admissible search directions and, in particular, to formulate optimality conditions. They no…
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.…