# DC Proximal Newton for Non-Convex Optimization Problems

arXiv: https://arxiv.org/abs/1507.00438 · HTML: https://mlsanity.com/paper/1507.00438/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2015.

## Built on by (most cited first, 1 of 1)

- [One-Step Forward and Backtrack: Overcoming Zig-Zagging in Loss-Aware Quantization Training](https://mlsanity.com/paper/2401.16760/) (2024)

## Abstract (arXiv)

We introduce a novel algorithm for solving learning problems where both the loss function and the regularizer are non-convex but belong to the class of difference of convex (DC) functions. Our contribution is a new general purpose proximal Newton algorithm that is able to deal with such a situation. The algorithm consists in obtaining a descent direction from an approximation of the loss function and then in performing a line search to ensure sufficient descent. A theoretical analysis is provided showing that the iterates of the proposed algorithm {admit} as limit points stationary points of the DC objective function. Numerical experiments show that our approach is more efficient than current state of the art for a problem with a convex loss functions and non-convex regularizer. We have also illustrated the benefit of our algorithm in high-dimensional transductive learning problem where both loss function and regularizers are non-convex.