# A Semismooth Newton Method for Support Vector Classification and Regression

arXiv: https://arxiv.org/abs/1903.00249 · HTML: https://mlsanity.com/paper/1903.00249/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2019.

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

- [Optimization Models and Interpretations for Three Types of Adversarial Perturbations against Support Vector Machines](https://mlsanity.com/paper/2204.03154/) (2022)
- [Robust and sparse support vector machine via hybrid truncated loss for supervised classification](https://mlsanity.com/paper/2606.05814/) (2026)

## Abstract (arXiv)

Support vector machine is an important and fundamental technique in machine learning. In this paper, we apply a semismooth Newton method to solve two typical SVM models: the L2-loss SVC model and the ε-L2-loss SVR model. The semismooth Newton method is widely used in optimization community. A common belief on the semismooth Newton method is its fast convergence rate as well as high computational complexity. Our contribution in this paper is that by exploring the sparse structure of the models, we significantly reduce the computational complexity, meanwhile keeping the quadratic convergence rate. Extensive numerical experiments demonstrate the outstanding performance of the semismooth Newton method, especially for problems with huge size of sample data (for news20.binary problem with 19996 features and 1355191 samples, it only takes three seconds). In particular, for the ε-L2-loss SVR model, the semismooth Newton method significantly outperforms the leading solvers including DCD and TRON.