摘要
本文提出了一种新的求解线性不等式组可行解的方法-动力系统方法.假设线性不等式组的可行域为非空,在可行域的相对内域上建立一个非线性极值问题,根据对偶关系,得到一个对偶空间的无约束极值问题以及原始、对偶变量之间的简单线性映射关系,进而得到了一个结构简单的动力系统模型.文中主要讨论了动力系统的隐式格式,通过证明模型具有较好的计算稳定性.同时,在寻找不等式组可行解的过程中,定义了穿越方向,这样可以减少计算量.数值实验结果表明此算法是有效的.
In this paper a new dynamical-system method for solving linear inequalities is presented. This method supposes that the feasible area of the linear inequalities is not empty, thus a nonlinear optimization problem is constructed on this non-empty area. Then, an unconstrained optimization problem and simple relation formula between original variable and dual variable are obtained according to the dual principle. A dynamical system modei of simple construction is obtained. In this paper an implied format is discussed and is proved to have a better stability of computing. During searching the feasible point, a new through direction is denned to decrease computing quantity. This method is proved effective by the numeral results.
出处
《系统科学与数学》
CSCD
北大核心
2004年第4期531-538,共8页
Journal of Systems Science and Mathematical Sciences
