三维空间中的黄金分割法

Golden-Section in Three Dimensional Space

给出求解无约束问题的一种新方法——三维空间上的黄金分割法,这是一种直接解法,该方法是一维搜索中的0.618法在空间中的推广,无需计算函数的导数,仅需计算函数值既可。此外,本法克服了以往直接解法所共有的要求大量计算机内存的缺点,所采用的迭代方法每次只需要处理一个长方体的数字信息,因而仅需占用极少的计算机内存,并且并不因此而降低计算效率。此外,还给出搜索过程的几何表示。

For solving unconstrained nonlinear optimization problems, a new algorithm, which is called Golden-section in three dimension, is presented. It is a kind of direct method and a extending of the 0.618 method in one-dimensional search in three-dimensional space. The derivative of objective function with respect to decision making variables is not needed to be calculated. On the other hand, this method needs so little memory that it almost can be implemented on any personal computer and its efficiency is not influenced. It works as well as grandient methods. Moreover, the geometric denotation of the process of searching is plotted.