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arXiv · 1608.03861

Another look at the fast iterative shrinkage/thresholding algorithm (FISTA)

Donghwan Kim·Jeffrey A. Fessler
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Abstract

This paper provides a new way of developing the fast iterative shrinkage/thresholding algorithm (FISTA) that is widely used for minimizing composite convex functions with a nonsmooth term such as the $\ell_1$ regularizer. In particular, this paper shows that FISTA corresponds to an optimized approach to accelerating the proximal gradient method with respect to a worst-case bound of the cost function. This paper then proposes a new algorithm that is derived by instead optimizing the step coefficients of the proximal gradient method with respect to a worst-case bound of the composite gradient mapping. The proof is based on the worst-case analysis called Performance Estimation Problem.

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Donghwan Kim, Jeffrey A. Fessler. 2018-01-23. Another look at the fast iterative shrinkage/thresholding algorithm (FISTA). https://doi.org/10.1137/16m108940x

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