# On the Convergence of the Iterative Shrinkage/Thresholding Algorithm With a Weakly Convex Penalty

arXiv: https://arxiv.org/abs/1510.07821 · HTML: https://mlsanity.com/paper/1510.07821/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2015.

## Built on by (most cited first, 6 of 6)

- [Nonconvex Regularization for Feature Selection in Reinforcement Learning](https://mlsanity.com/paper/2509.15652/) (2025)
- [Playing the Lottery With Concave Regularizers for Sparse Trainable Neural Networks](https://mlsanity.com/paper/2501.11135/) (2025)
- [Fast sparse optimization via adaptive shrinkage](https://mlsanity.com/paper/2501.12236/) (2025)
- [Proximal Operators of Sorted Nonconvex Penalties](https://mlsanity.com/paper/2506.15315/) (2025)
- [Non-Convex Sparse Reinforcement Learning via Non-Monotone Inclusions](https://mlsanity.com/paper/2607.04990/) (2026)
- [A proximal subgradient method for nonconvex stochastic optimization under the Kurdyka-Lojasiewicz condition](https://mlsanity.com/paper/2608.05460/) (2026)

## Abstract (arXiv)

We consider the iterative shrinkage/thresholding algorithm (ISTA) applied to a cost function composed of a data fidelity term and a penalty term. The penalty is non-convex but the concavity of the penalty is accounted for by the data fidelity term so that the overall cost function is convex. We provide a generalization of the convergence result for ISTA viewed as a forward-backward splitting algorithm. We also demonstrate experimentally that for the current setup, using large stepsizes in ISTA can accelerate convergence more than existing schemes proposed for the convex case, like TwIST or FISTA.