8 citations · 29 across the 13 of their papers we have counts for
12 papers · 1 filter
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…
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.…