# Non-smooth Non-convex Bregman Minimization: Unification and new Algorithms

arXiv: https://arxiv.org/abs/1707.02278 · HTML: https://mlsanity.com/paper/1707.02278/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2017.

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

- [Sharper Bounds for Proximal Gradient Algorithms with Errors](https://mlsanity.com/paper/2203.02204/) (2022)
- [Robust Regression via Model Based Methods](https://mlsanity.com/paper/2106.10759/) (2021)

## Abstract (arXiv)

We propose a unifying algorithm for non-smooth non-convex optimization. The algorithm approximates the objective function by a convex model function and finds an approximate (Bregman) proximal point of the convex model. This approximate minimizer of the model function yields a descent direction, along which the next iterate is found. Complemented with an Armijo-like line search strategy, we obtain a flexible algorithm for which we prove (subsequential) convergence to a stationary point under weak assumptions on the growth of the model function error. Special instances of the algorithm with a Euclidean distance function are, for example, Gradient Descent, Forward--Backward Splitting, ProxDescent, without the common requirement of a "Lipschitz continuous gradient". In addition, we consider a broad class of Bregman distance functions (generated by Legendre functions) replacing the Euclidean distance. The algorithm has a wide range of applications including many linear and non-linear inverse problems in signal/image processing and machine learning.