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Conference Papers Year : 2011

Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization

Abstract

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.
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Dates and versions

inria-00618152 , version 1 (12-09-2011)
inria-00618152 , version 2 (01-12-2011)
inria-00618152 , version 3 (01-12-2011)

Identifiers

  • HAL Id : inria-00618152 , version 3
  • ARXIV : 1109.2415

Cite

Mark Schmidt, Nicolas Le Roux, Francis Bach. Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization. NIPS'11 - 25 th Annual Conference on Neural Information Processing Systems, Dec 2011, Grenada, Spain. ⟨inria-00618152v3⟩
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