两类逼近精确罚函数法及其数值试验

1 引言 精确罚函数(exact penalty function)的构造主要有两条途径:一是基于Lagrange乘子的乘子罚函数方法,二是直接构造非光滑的精确罚函数。不必进行乘子迭代。本文讨论第三种思路:基于目标函数最优值构造保持光滑性的精确罚函数。某些无参数外点罚函数本应属于此类,但一直仅仅被作为普通外点罚函数的无参数形式。将其与无参 数内点罚函数同等看待,因此基于目标函数最优值构造精确罚函数未得到充分研究。文献[11]给出了初步结果。本文进一步发展了有关理论,导出了两类算法,证明了收敛性,最后给出了数值试验结果。 2 基于目标函数最优值的精确罚函数 考虑如下约束优化问题

TWO CLASSES OF APPROXIMATING EXACT PENALTY FUNCTION ALGORITHMS WITH THEIR NUMERICAL EXPERIMENTS

This paper presents two classes of exact penalty function algorithms based on the optimal value of the objective function: the algorithm approximating the opti-mal point from "both sides" and the algorithm approximating from "outside". The convergence of the algorithms is proved. The superiority of the first algorithm in solving very difficult problems has been verified by the numerical experiments.