线性支持向量机优化问题的一种光滑算法

Smoothing algorithm for linear Support Vector Machine

线性支持向量机的无约束优化模型的目标函数不是一个二阶可微函数,因此不能应用一些快速牛顿算法来求解。提出了目标函数的一种光滑化技巧,从而得到了相应的光滑线性支持向量机模型,并给出了求解该光滑线性支持向量机模型的Newton-Armijo算法,该算法是全局收敛的和二次收敛的。

The objective function in the unconstrained model of linear Support Vector Machine （SVM） is not twice differentiable which precludes the use of a fast Newton method.In this paper,a type of smoothing technique is proposed to overcome the difficulty.By using the smoothing technique,a smoothing SVM model is obtained.A Newton-Armijo algorithm which is globally and quadratically convergent is given to solve the smoothing SVM model.