| Autor: |
Attouch, Hedy, Peypouquet, Juan |
| Rok vydání: |
2015 |
| Předmět: |
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| Zdroj: |
SIAM Journal on Optimization 26 (2016), no. 3, 1824-1834 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1137/15M1046095 |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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