一类广义半无限规划问题的光滑牛顿算法

A SMOOTHING NWETON METHOD FOR GENERAL SEMI-INFINITE PROGAMMING

本文在广义半无限规划问题的最优解集X*处满足某些条件的前提下将广义半无限规划问题转化成KKT系统,通过扰动的FB函数,将KKT系统转化为一组光滑函数方程,设计了一个光滑牛顿算法,证明了算法的全局收敛性,并且在光滑函数解集处满足局部误差界条件下证明了算法具有超线性收敛速率.

In this paper we reformulate the GSIP problems into a KKT system under some conditions at the set X that is the set of local minimizers of GSIP problems.By using a peturbed Fisher-Burmeister function,we reformulate the KKT system into system of smooth equations,and we design a smoothing Newton method for solving this system,then we prove the method is globally and under a cocal error bound condition for the system of smooth equations the method is superlinearly convergent