正基与一类直接搜索法

本文对非线性规划中的一类直接搜索法给出了一个统一的收敛定理,这类方法被称为定步长下山法,它包括了轴向搜索法、Hooke-Jeeves方法以及对Hooke-Jeeves方法所作的简化与变形(文中给出)作为特例,从而这些算法的收敛性质均能根据上述统一的收敛定理得到,除了这些以外,单纯形调优法也能用同样的想法来进行分析,这由作者在另一文中给出,为了上述目的,本文还对代数中的正基作了若干研究。

POSITIVE BASIS AND A CLASS OF DIRECT SEARCH TECHNIQUES

A unified convergent theorem is given for a class of direct scarch techniques in nonlinear programming. This class of techniques is defined as the descent method with fixed step size. It tins the following techniques as its special cases: the axis directional search technique, Hooke-Jeeves technique and the simplified and varied Hooke-Jeeves techniques given, in this paper. Thus the convergence of these techniques can be obtained from the above unified convergent theorem. Besides, the same idea may be applied to the analysis of the simplex evolutionary technique which will be given by the author in a separate paper. For these purposes, a study of positive basis in algebra is made in the first part of this paper.