1 code implementation • 25 Jan 2021 • Cyrille W. Combettes, Sebastian Pokutta
The Frank-Wolfe algorithm is a method for constrained optimization that relies on linear minimizations, as opposed to projections.
1 code implementation • 29 Sep 2020 • Cyrille W. Combettes, Christoph Spiegel, Sebastian Pokutta
The complexity in large-scale optimization can lie in both handling the objective function and handling the constraint set.
1 code implementation • ICML 2020 • Cyrille W. Combettes, Sebastian Pokutta
The Frank-Wolfe algorithm has become a popular first-order optimization algorithm for it is simple and projection-free, and it has been successfully applied to a variety of real-world problems.
1 code implementation • 11 Nov 2019 • Cyrille W. Combettes, Sebastian Pokutta
The approximate Carath\'eodory theorem states that given a compact convex set $\mathcal{C}\subset\mathbb{R}^n$ and $p\in\left[2,+\infty\right[$, each point $x^*\in\mathcal{C}$ can be approximated to $\epsilon$-accuracy in the $\ell_p$-norm as the convex combination of $\mathcal{O}(pD_p^2/\epsilon^2)$ vertices of $\mathcal{C}$, where $D_p$ is the diameter of $\mathcal{C}$ in the $\ell_p$-norm.
no code implementations • NeurIPS 2019 • Cyrille W. Combettes, Sebastian Pokutta
Matching pursuit algorithms are an important class of algorithms in signal processing and machine learning.