Abstract: Smooth Support Vector Classification（SSVC） originally is unconstrained mathematical programming with convex and smooth，and is a method for solving Support Vector Classification（SVC） quickly.The BFGS-Armijo and Newton-Armijo algorithms have been used to train SSVC，and the latter has faster speed.Newton-PCG algorithm is just enough method for unconstrained problem which has better speed than Newton in theory.On the numerical experimentation of using BFGS-Armijo，Newton-Armijo and Newton-PCG to train SSVC，this paper gives analysis and comparison among the three algorithms，and proves that Newton-PCG has the best result.

Key words: pattern recognition, Smooth Support Vector Machine（SSVM）, classification, Newton-PCG

摘要： 光滑支持向量分类机（SSVC）是支持向量分类机（SVC）的快速求解模型，本质上是求解数学规划中具有光滑性和强凸性的无约束最优化问题。BFGS-Armijo和Newton-Armijo算法被用来训练SSVC，相比而言后者拥有更快的训练速度；牛顿-预优共轭梯度法（Newton-PCG）适用于求解无约束的最优化问题，理论上快于一般的Newton类算法。使用Newton-Armijo、BFGS-Armijo和Newton-PCG三种算法来训练光滑支持向量分类机，根据数值实验结果进行分析比较，证明了Newton-PCG算法有更优的效果。

关键词: 模式识别, 光滑支持向量机, 分类, Newton-PCG算法