GSVM优化问题的一种新的光滑函数法

Smoothing function method for generalized support vector machine optimization problems

提出求解广义支撑向量机(GSVM)优化问题的一种新的光滑函数法,克服了已有算法收敛速度慢且计算结构复杂的缺陷。首先利用最优化理论的KKT互补条件,将GSVM转化为无约束优化问题,然后给出了基于Newton型迭代的光滑函数的迭代方法。给出了这种光滑函数的有关性质、迭代算法的迭代格式及其收敛性。通过理论分析及数值实验证明了该算法对初始点不敏感,且收敛速度快、数值稳定。从而验证了算法的可行性和有效性。

Novel soothing function method for generalized support vector machine （GSVM） is proposed and attempts some drawbacks of former method which are complex, subtle, and sometimes difficult to implement. First, used KKT complementaritys condition in optimization theory, unconstrained nondifferential optimization model are built. Then approximate function is given. Finally, the data set with standard unconstraint optimization Newton method is trained. The property of the smoothing function and convergence of the algorithm are obtained. This algorithm is fast and insensitive to initial point. Theory analysis and primary numerical results illustrate that smoothing function method for GSVM is feasible and effective.