786 citations · 2.1k across the 40 of their papers we have counts for
5 papers · 2 filters
Quadproj: a Python package for projecting onto quadratic hypersurfaces
Loïc Van Hoorebeeck, P. -A. Absil
Quadratic hypersurfaces are a natural generalization of affine subspaces, and projections are elementary blocks of algorithms in optimization and machine learning. It is therefore…
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…
Projection onto quadratic hypersurfaces
Loïc Van Hoorebeeck, P. -A. Absil, Anthony Papavasiliou
We address the problem of projecting a point onto a quadratic hypersurface, more specifically a central quadric. We show how this problem reduces to finding a given root of a scala…
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…
Optimization flows landing on the Stiefel manifold
Bin Gao, Simon Vary, Pierre Ablin +1
We study a continuous-time system that solves optimization problems over the set of orthonormal matrices, which is also known as the Stiefel manifold. The resulting optimization fl…