通过平衡点求线性二层规划(LBP)的最优解

Finding the Optimal Solution of Linear Bilevel Program by the Equilibrium Point

关于线性二层规划的求解问题。先利用K-T充分条件和罚函数法先将线性二层规划转化为无约束问题,再由无约束问题得到简单的参数线性规划,通过单纯形法解参数线性规划,即得到平衡点,再判断平衡点是否为原二层规划的最优解。

In this paper,linear bilevel programming problem （LBP） is considered. The first, （LBt＇） is changed into no constrained problem by K- T conditions and the penalized method, then, change the no constrained problem into the parametric linear program, and find the solutions of the parametric linear program by the simplex method, the solutions is just the equilibrium point, last, determine which equilibrium point is the optimal solution of LBP.