求解线性不等式组的方法

本提出了一个新的求解线性不等式组可行解的方法－－无约束极值方法。通过在线性不等式组的非空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，得到了一个对偶空间的无约束极值及原始，对偶变量之间的简单线性映射关系，这样将原来线性不等式组问题的求解转化为一个无约束极值问题。中主要讨论了求解无约束极值问题的共轭梯度算法。同时，在寻找不等式组可行解的过程中，定义了穿越方向，这样大大减少计算量。中最后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 effectively proved by the numeral results at the end of this paper.