求解广义非线性互补问题的光滑化拟牛顿法

Smoothing quasi-Newton method for generalized nonlinear complementarity problems

利用光滑对称扰动Fischer-Burmeister函数将广义非线性互补问题转化为非线性方程组,提出新的光滑化拟牛顿法求解该方程组.然后证明该算法是全局收敛的,且在一定条件下证明该算法具有局部超线性(二次)收敛性.最后用数值实验验证了该算法的有效性.

Using the smoothing symmetrical perturbation Fischer-Burmeister function,we can reformulate the generalized nonlinear complementarity problem as a nonsmooth system of equations. A new smoothing Quasi-Newton method for solving the system of equations is presented.Then,the global convergence properties of this algorithm are proved,and the superlinearly convergence can be proved under mild assumptions.At last,numerical experiments show that the algorithm is feasible and effective.