# Proximal gradient method for huberized support vector machine

arXiv: https://arxiv.org/abs/1511.09159 · HTML: https://mlsanity.com/paper/1511.09159/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2015.

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

- [Parallel Algorithms for Structured Sparse Support Vector Machines: Application in Music Genre Classification](https://mlsanity.com/paper/2512.07463/) (2025)
- [Is Fairness Truly Fair? Towards Reliable Lipschitz Fairness in Multi-Task Learning via Fixed-texorpdfstringδdelta Alignment](https://mlsanity.com/paper/2606.10632/) (2026)

## Abstract (arXiv)

The Support Vector Machine (SVM) has been used in a wide variety of classification problems. The original SVM uses the hinge loss function, which is non-differentiable and makes the problem difficult to solve in particular for regularized SVMs, such as with ℓ1-regularization. This paper considers the Huberized SVM (HSVM), which uses a differentiable approximation of the hinge loss function. We first explore the use of the Proximal Gradient (PG) method to solving binary-class HSVM (B-HSVM) and then generalize it to multi-class HSVM (M-HSVM). Under strong convexity assumptions, we show that our algorithm converges linearly. In addition, we give a finite convergence result about the support of the solution, based on which we further accelerate the algorithm by a two-stage method. We present extensive numerical experiments on both synthetic and real datasets which demonstrate the superiority of our methods over some state-of-the-art methods for both binary- and multi-class SVMs.