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arXiv · 1109.2415

Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization

Mark Schmidt·Nicolas Le Roux·Francis Bach
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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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Mark Schmidt, Nicolas Le Roux, Francis Bach. 2011-12-01. Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization. https://arxiv.org/abs/1109.2415

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