ANOTHER LOOK AT THE FAST ITERATIVE SHRINKAGE/THRESHOLDING ALGORITHM (FISTA)
This paper provides a new way of developing the "Fast Iterative Shrinkage/Thresholding Algorithm (FISTA)" [3] that is widely used for minimizing composite convex functions with a nonsmooth term such as the ℓ regularizer. In particular, this paper shows that FISTA corresponds to an optimize...
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| Published in | SIAM journal on optimization Vol. 28; no. 1; p. 223 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
United States
2018
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| Online Access | Get more information |
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| Summary: | This paper provides a new way of developing the "Fast Iterative Shrinkage/Thresholding Algorithm (FISTA)" [3] that is widely used for minimizing composite convex functions with a nonsmooth term such as the ℓ
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 in [11]. |
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| ISSN: | 1052-6234 |
| DOI: | 10.1137/16M108940X |