对下楼法的进一步讨论

A FURTHER APPROACH TO THE DOWNSTAIRS METHOD FOR FINDING GLOBAL MINIMIZERS OF A FUNCTION

引言为求一个多元函数的总体极小点,在[1]中作者提出了一种新方法——下楼法(简称DSM法)。但还有三个问题没解决。 1)在找到函数的一个局部极小点之后,我们构造了一个非线性方程组,如何去判断这个方程组是否有解? 2)如果上述方程组有解存在,用什么方法可以一定把解求出来? 3)用DSM法时怎么才能判断出我们已经找到了函数的总体极小点?换句话说。

The three remaining problems in the downstairs method (DSM) proposed by the author (1), which finds a global minimizer of nonlinear functions of several variables by finding lower and lower minimizers, are dealt with theoretically in this paper. The solutions to the problems make DSM perfect. Under some conditions it guarantees the finding of a global minimum point of a nonlinear function or its good approximation and also gives the criterion for terminating the algorithm. In addition, this method can be used to deal with functions not only in the multidimensional case but also in the one-dimensional case.