HAL: inria-00618152, version 3

arXiv: 1109.2415

See detailed view

BibTeX,EndNote,... BibTeX - EndNote - TEI - RefWorks -

NIPS'11 - 25 th Annual Conference on Neural Information Processing Systems, Grenada : Espagne (2011)

Available versions

v1 (2011-09-12)

v2 (2011-12-01)

v3 (2011-12-01)

Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization

Mark Schmidt (  Author to contact preferably ) 1, 2, Nicolas Le Roux 1, 2, Francis Bach 1, 2

(2011-12)

We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity operator with respect to the non-smooth term. We show that both the basic proximal-gradient method and the accelerated proximal-gradient method achieve the same convergence rate as in the error-free case, provided that the errors decrease at appropriate rates.Using these rates, we perform as well as or better than a carefully chosen fixed error level on a set of structured sparsity problems.

1:	SIERRA (INRIA Paris - Rocquencourt)
	INRIA : PARIS - ROCQUENCOURT – Ecole normale supérieure de Paris - ENS Paris – CNRS : UMR8548
2:	Laboratoire d'informatique de l'école normale supérieure (LIENS)
	CNRS : UMR8548 – Ecole normale supérieure de Paris - ENS Paris

Domain

:

Computer Science/Learning Mathematics/Optimization and Control

Keywords: optimization – proximal method – convexity – strong convexity – accelerated method – convergence rate

inria-00618152, version 3

http://hal.inria.fr/inria-00618152

oai:hal.inria.fr:inria-00618152

From: Nicolas Le Roux <>

Submitted on: Thursday, 1 December 2011 16:03:15

Updated on: Tuesday, 20 December 2011 09:42:09