摘要
一般常见的外罚函数φ(X,r^(K))在可行域外的性质极为复杂,其海赛矩阵H(X)的病态随罚因子r^(K)趋向无穷大而逐渐增加,使迭代困难,甚至可能失败。同时,R^((K))的选择也无确定有效的规则。由于φ(X,r^(K))对初始点要求不严格,所以研究避免r^(K)对φ(X,r^(K))产生病态影响而构造新的外罚函数成为共同关切的问题。本文对文献[1]提出的新的外罚函数φ(X,β^(K))在结构性能、几何特性,迭代方法方面进行了分析,并以算例进行了考核,揭示了φ(X,β^(K))与中(X,R^(K))之间的区别和联系,为扩大外罚法的应用范围提供了一个新的途径。
The general exterior penalty function φ(X,r^(K))has very complicated properties outside the feasible region.The ill- condition of its Hessian matrix H(X)of φ(X,r^(K))increases as the penalty factor r^(K)tends to infinite,which makes the numerical iteration difficult,or even unsuccessful.Moreover, there is no definitely effective rule to choose r^(K)However, since φ(X,β^(K))is not critical for the choice of initial points, it has become a commonly concerned problem to search for a new exterior penalty function that can avoid the effect of ill- condition of φ(X,r^(K))caused by r^(K). In this paper,we analyze the structure,performance behavior, geometric characteristic and iterative process of the new exterior panalty function φ(X,β^(K))suggested in[1].Differences and relations between φ(X,β^(K))and φ(X,r^(K))are also discussed. Finally we examine some example and thereby provide a new approach to extend the application area of exterior penalty function methods.
出处
《长沙铁道学院学报》
CSCD
1990年第1期35-40,共6页
Journal of Changsha Railway University
关键词
非线性规划
外罚函数
优化设计
Optimum Design
Non-Linear Programming
exterior penalty function
