求解线性二层规划的一种全局优化方法

A Globally Convergent Method for Solving Linear Bilevel Programming Problem

以下层问题的KT最优性条件代替下层问题,同时取互补条件为罚项,将线性二层规划转化为带线性互补约束条件的单层优化问题。通过分析单层优化问题与线性二层规划问题之间的关系,将线性二层规划等价地转化为有限个线性规划,通过求解有限个线性规划问题,就得到了线性二层规划问题的最优解。该方法不但能够得到线性二层规划问题的全局最优解,而且还简化了最优解判别条件。

Following the method of replacing the lower level problem with its Kuhn-Tuck optimality condition,we get the optimization programming problem with linear complementary constraints.By analyzing the relationship between the linear bilevel programming problem and the corresponding one level programming problem,we transform the linear bilevel programming problem into a series of linear programming problems equivalently.Then,we get the global optimal solution of the linear bilevel programming using linear programming method.