“二维LP问题的一个直接算法”中定理反例

The Counter-examples of Theorem in "A Direct Algorithm of Two-Dimensional Linear Programming Questions"

针对"二维LP问题的一个直接算法"一文中的算法基本定理,给出了两个反例,分别说明其中的引理和定理都是错误的,建立在这些结论基础上的求解一般线性规划问题的代数算法无法求出一般线性规划问题的最优解。数值试验表明,随着方程个数的增加,用他们的方法求得正确解的概率将越来越低。给出了一个二维线性规划问题最优解的性质定理,由该定理可导出文[1]中代数算法有效的条件。

Aim at the lemma and theorem in ＂A Direct Algorithm of Two-Dimensional Linear Programming Questions＂, two counter- examples are given to show the lemma and theorem are wrong respectively, therefore the alglebraic algorithm given by them unable to find out the optimal solution of two-dimensional linear programming problem.Numerical experiments show that, with the increasing of the equation＇s number, the probability of obtaining the correct solution by their algorithm will reduce.A property theorem about optimum solution of two-dimensional linear programming questions is given, the condition which the alglebraic algorithm is effective is reduced.