对偶单纯形法的一点补充

A Supplement to Dual Simplex Method

管梅谷，郑汉鼎在《线性规划》中指出：如果初始基本解不是正则解，那么可以增加一个约束（含一个大数Ｍ）．这个增加了约束的新问题叫做扩充问题．可以用对偶单纯形法解此扩充问题．作者指出：如果扩充问题的最优目标值不含Ｍ，则原问题有最优解．本文进一步指出并证明：如果扩充问题的最优目标值含有Ｍ。

Chapter Five in Linear Programming by Guan Meigu and Zhen Hanjing points out:if an initial basic solution is not regular solution,then we can add a constraint(containing a large number M).This new problem is called extended problem which can be solved by the dual simplex method. The author points out:if the optional objective value of the extended problem does not contain M,then the primal problem has optiomal solution.The paper further proves:if the optiomal objective value contains M,then the primal problem doesn't have finite optimal solution.