# An inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions

arXiv: https://arxiv.org/abs/1410.0641 · HTML: https://mlsanity.com/paper/1410.0641/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2014.

## Built on by (most cited first, 8 of 8)

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- [Inertial Newton Algorithms Avoiding Strict Saddle Points](https://mlsanity.com/paper/2111.04596/) (2021)
- [Universal and Transferable Adversarial Attack on Large Language Models Using Exponentiated Gradient Descent](https://mlsanity.com/paper/2508.14853/) (2025)
- [On Information Geometry and Iterative Optimization in Model Compression: Operator Factorization](https://mlsanity.com/paper/2507.09428/) (2025)
- [A Proximal Modified Quasi-Newton Method for Nonsmooth Regularized Optimization](https://mlsanity.com/paper/2409.19428/) (2024)

## Abstract (arXiv)

We propose a forward-backward proximal-type algorithm with inertial/memory effects for minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting. The sequence of iterates generated by the algorithm converges to a critical point of the objective function provided an appropriate regularization of the objective satisfies the Kurdyka-Lojasiewicz inequality, which is for instance fulfilled for semi-algebraic functions. We illustrate the theoretical results by considering two numerical experiments: the first one concerns the ability of recovering the local optimal solutions of nonconvex optimization problems, while the second one refers to the restoration of a noisy blurred image.