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

arXiv: https://arxiv.org/abs/1608.03861 · HTML: https://mlsanity.com/paper/1608.03861/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Aug 2016.

## Built on by (most cited first, 2 of 2)

- [Practical Schemes for Finding Near-Stationary Points of Convex Finite-Sums](https://mlsanity.com/paper/2105.12062/) (2021)
- [Simpler Methods Work Better for L1 Penalized Logistic Models and Large Datasets](https://mlsanity.com/paper/2609.23995/) (2026)

## Abstract (arXiv)

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 ℓ1 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.