线性圆锥互补问题的光滑化牛顿法

Smoothing Newton Method for Linear Circular Cone Complementarity Problems

给出求解线性圆锥互补问题一种新的光滑化牛顿法.首先,基于一个圆锥互补函数的光滑化函数,将线性圆锥互补问题转化成一个方程组,然后用光滑化牛顿法求解该方程组;其次,在适当假设下,证明该算法具有全局收敛性和局部二阶收敛性.数值结果表明,该算法求解线性圆锥互补问题所需的CPU时间和迭代次数均较少,且相对稳定,从而证明了算法的有效性.

We presented a new smoothing Newton method for solving the linear circular cone complementarity problems.Firstly,based on the smoothing function of the circular cone complementary function,the linear circular cone complementarity problem was transformed into a system of equations,which were solved by the smoothing Newton method.Secondly,under suitable assumptions,we proved that the algorithm had the global convergence and local quadratic convergence.The numerical results show that the CPU time and iteration times of the algorithm for solving linear circular cone complementarity problems are less,and the algorithm is relatively stable,which proves the effectiveness of the algorithm.