- The rate of convergence of Nesterov's accelerated forward-backward method is actually $o(k^{-2})$ H Attouch (hedy.attouchuniv-montp2.fr) J Peypouquet (juan.peypouquetusm.cl) Abstract: The {\it forward-backward algorithm} is a powerful tool for solving optimization problems with a {\it additively separable} and {\it smooth} + {\it nonsmooth} structure. In the convex setting, a simple but ingenious acceleration scheme developed by Nesterov has been proved useful to improve the theoretical rate of convergence for the function values from the standard $\mathcal O(k^{-1})$ down to $\mathcal O(k^{-2})$. In this short paper, we prove that the rate of convergence of a slight variant of Nesterov's accelerated forward-backward method, which produces {\it convergent} sequences, is actually $o(k^{-2})$, rather than $\mathcal O(k^{-2})$. Our arguments rely on the connection between this algorithm and a second-order differential inclusion with vanishing damping. Keywords: Convex optimization, fast convergent methods, Nesterov method Category 1: Convex and Nonsmooth Optimization (Convex Optimization ) Citation: Download: [PDF]Entry Submitted: 10/29/2015Entry Accepted: 10/29/2015Entry Last Modified: 11/01/2015Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.