线性规划问题有无穷多个最优解的条件

A Condition under which Linear Programming Problem has Infinite Number of Optimal Solutions

本文给出线性规划问题有无穷多个最优解的必要条件,并且证明在非退化的情况下,这个条件也是充分的。这个条件是:在最终单纯形表中存在非基变量x_k,其检验数λ_k=0且b_(ik)(1≤i≤m)不全小于等于0。

In this paper a necessary condition under which linear programming problem has infinite number of optimal solutions is given, and it is proven that in nondegenerate case the condition is also sufficient. This condition is that in eventual simplex tabuleau there exists nonbasic variable x_k with check number λ_k=0, and there are some b_(ik)(l≤i≤m) greater than zero.