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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 common external penalty function φ(X,rK) is very complex outside the feasible region. The pathological state of the H.S. matrix H(X) gradually increases with the infinity of the penalty factor r~(K), making iterative Difficulties may even fail. At the same time, the choice of R((K)) does not determine the effective rule. Since φ(X,rK) is not strict with the initial point, it is a common concern to study how to avoid the influence of r~(K) on φ(X,rK) and construct a new external penalty function. The problem. In this paper, the new external penalty function φ(X,β~(K)) proposed in [1] is analyzed in terms of structural properties, geometrical characteristics, and iterative methods, and evaluated by an example to reveal φ(X). The difference and connection between ~β(K)) and 中(X,R (K) provides a new way to expand the scope of application of the external penalty method.