同解视角下对单纯形法的理解

摘要

After the elementary transformation of the augmented matrix of linear equations, the transformed equation system and the original linear equation system are equivalent.With the aid of the theory above, the new matrix could be formed based on the augmented matrix of objective function and constraint condition in standard form of linear programming.Then, after the elementary transformation on the new matrix by the way of basis iteration and meeting certain requirements, the optimal solution in linear programming could be obtained by the transformed matrix.%对线性方程组的增广矩阵实施初等变换,变换后所对应方程组与原线性方程组同解.借助该理论,将线性规划问题标准型中的目标函数系数及约束条件中的增广矩阵按一定方法组成新的矩阵,通过基变量的换基迭代原理对新矩阵进行初等变换,符合一定要求后,通过变换后的矩阵求出线性规划问题的最优解.