11 citations · 45 across the 21 of their papers we have counts for
8 papers · 1 filter
Strong Convexity of Sets in Riemannian Manifolds
Damien Scieur, David Martínez-Rubio, Thomas Kerdreux +2
Curvature properties of convex objects, such as strong convexity, are important in designing and analyzing convex optimization algorithms in the Hilbertian or Riemannian settings.…
Acceleration of Frank-Wolfe Algorithms with Open-Loop Step-Sizes
Elias Wirth, Thomas Kerdreux, Sebastian Pokutta
Frank-Wolfe algorithms (FW) are popular first-order methods for solving constrained convex optimization problems that rely on a linear minimization oracle instead of potentially ex…
Local and Global Uniform Convexity Conditions
Thomas Kerdreux, Alexandre d'Aspremont, Sebastian Pokutta
We review various characterizations of uniform convexity and smoothness on norm balls in finite-dimensional spaces and connect results stemming from the geometry of Banach spaces w…
Affine Invariant Analysis of Frank-Wolfe on Strongly Convex Sets
Thomas Kerdreux, Lewis Liu, Simon Lacoste-Julien +1
It is known that the Frank-Wolfe (FW) algorithm, which is affine-covariant, enjoys accelerated convergence rates when the constraint set is strongly convex. However, these results…
Projection-Free Optimization on Uniformly Convex Sets
Thomas Kerdreux, Alexandre d'Aspremont, Sebastian Pokutta
The Frank-Wolfe method solves smooth constrained convex optimization problems at a generic sublinear rate of , and it (or its variants) enjoys accelerated converg…
Restarting Frank-Wolfe: Faster Rates Under Hölderian Error Bounds
Thomas Kerdreux, Alexandre d'Aspremont, Sebastian Pokutta
Conditional Gradient algorithms (aka Frank-Wolfe algorithms) form a classical set of methods for constrained smooth convex minimization due to their simplicity, the absence of proj…
Frank-Wolfe with Subsampling Oracle
Thomas Kerdreux, Fabian Pedregosa, Alexandre d'Aspremont
We analyze two novel randomized variants of the Frank-Wolfe (FW) or conditional gradient algorithm. While classical FW algorithms require solving a linear minimization problem over…
An Approximate Shapley-Folkman Theorem
Thomas Kerdreux, Igor Colin, Alexandre d'Aspremont
The Shapley-Folkman theorem shows that Minkowski averages of uniformly bounded sets tend to be convex when the number of terms in the sum becomes much larger than the ambient dimen…