单纯形调优法的收敛性质

在非线性规划中,单纯形调优法是一种可信用的算法,然而却缺乏理论分析,本文对单纯形调优法的理论进行了一些研究,所考虑的方法类似于Spendley,Hext,Himsworth的正规单纯形调优法,但采用了不同的反映条件,其中带有某种下山门槛或具有三点下降形式,这里的基本思想是证明:上述单纯形调优法是定步长下山法的特殊情形,所以,此研究紧密联系着作者关于定步长下山法收敛定理的工作。

THE CONVERGENTE PROPERTY OF THE SIMPLEX EVOLUTIONARY TECHNIQUE

The simplex evolutionary technique is a reliable algorithm in nonlinear program-ruing, but no theoretical analysis has been given for it. In this paper, a discussion is given on the theory of the simplex evolutionary technique., The technique considered are similar to the regular simplex evolutionary technique of Spendley, Hext. and Himsworth, but a different reflection condition, involving some descent threshold or three-point descent form is used. The basic idea here is to prove that the simplex evolutionary technique is the special case of the so-called descent method with fixed step size. Therefore, the study is closely related to the author''s work on the unified convergence theorem of descent method with fixed step size.