基于动力系统的线性不等式组的解法

本文提出了一种新的求解线性不等式组可行解的方法-基于动力系统的方法．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关系表达式,进而得到一个结构简单的动力系统模型．同时,定义了穿越方向。文章最后的数值实验结果表明此算法是有效的．

A New Method for Solving Linear Inequalities

In this paper, a new method of unconstrained optimization algorithm for solving linear inequalities problem is presented. A nonlinear optimization problem is constructed on the non-empty feasible area. Thus, an unconstrained optimization problem and simple relation form between x and y is attained by the dual principle. Then linear inequalities problem is thus transferred to an unconstrained optimization problem. There are many methods to solve the optimization problems. Conjugate gradient method is applied in this paper. At the same time, a new condition of through direction is proposed, thus much work would be decreased in the computing process. The unconstrained optimization algorithm is effective proved by the numeral results in the end of this paper.