支持向量机的一步光滑牛顿法

基于支持向量机的一个修正模型,将支持向量机优化问题转化为与之对偶规划等价的互补问题,简化了原二次规划问题.并利用Fischer-Burmeister互补函数,给出了一个求解该问题的一步光滑化牛顿算法.该算法每次迭代只需求解一个线性方程组,执行一次线性搜索,提高了运算效率,且算法可以任意选取初始点并具有二次收敛性质.初步的仿真实验表明该算法是可行有效.

One-step Smoothing Newton Method for Support Vector Machines

Based on the amended quadratic programming problem of support vector machines.The trans-formation of the optimization problem of the support vector machines into a complementarity problem,which is equivalent to the dual problem of the amended quadratic programming problem,simplifies the primal problem.By using the Fischer-Burmeister complementarity function,a one-step smoothing Newton method is presented.The proposed algorithm solves one only linear system of equations and performs only one linear search at each iteration.This algorithm does not have restriction on the start point and has the property of quadratic convergence.Preliminary numerical experiments show that the method is feasible and effective.