Luis Briceño-Arias
Speaker: Luis Briceño-Arias (Universidad Técnica Federico Santa María, Chili)
Title: Theoretical and numerical comparison of algorithms for smooth optimization
Abstract: In this talk, we provide a theoretical and numerical comparison of classical first-order splitting methods for solving smooth convex optimization problems. Theoretically, we compare convergence rates of gradient descent, forward-backward, Peaceman-Rachford, and Douglas-Rachford algorithms for minimizing the sum of two smooth convex functions when one is strongly convex. In several instances, we obtain improved rates with respect to the literature by exploiting the structure of our problems. Moreover, we indicate which algorithm has the lowest convergence rate depending on the strong convexity parameter and the Lipschitz constant of the gradient. From a numerical point of view, we verify our theoretical results by implementing and comparing previous algorithms in well-established signal and image inverse problems involving sparsity. We replace the widely used ℓ1 norm with the Huber loss and we observe that fully proximal-based strategies have numerical and theoretical advantages with respect to methods using gradient steps.
Refs : L. M. Briceño-Arias and N. Pustelnik, Theoretical and numerical comparison of first-order algorithms for cocoercive equations and smooth convex optimization, Signal Processing, vol. 206, no. C, May 2023.
More information: https://scholar.google.com/citations?user=YLin4W4AAAAJ&hl=en
Talk in room M7 101 (Campus Monod, ENS de Lyon)