线性二级规划问题的一种解法

AN ALGORITHM FOR THE LINEAR BILEVEL PROGRAMMING PROBLEM

本文以线性二级规划问题（ＬＢＰ）解的可行性条件和罚函数方法为基础，提出了一种只要用单纯形法解有限个线性规划问题，总可以找到ＬＢＰ的极最优解的解线性二级规问题的方法．这些线性规划问题很容易构造出来，整个计算是程式化的，很容易编制计算机程序，迭代步骤一般相当少．

Many solution approaches for the linear bilevel programming problem (LBP) have been developed to date, the amount of work required to find a solution seems to fast with the dimension of the underlying polyhedral constraint set. In this paper, first-order necessary an sufficient conditions is first employed to transform BLP into maxi-maxi problem, Necessary and sufficient conditions for optimality are derived Next, and algorithm to solve linear bilevel programming poblem is presented, it is needed only to solve several linear programming problem by simplex method. In general, iterative process in this algorithm is shorter.