非线性二层规划问题的全局优化方法

A GLOBAL CONVERGENT METHOD FOR NONLINEAR BILEVEL PROGRAMMING PROBLEM

对于下层为线性规划问题的一类非线性二层规划问题,利用线性规划的对偶理论,将其转化为一个单层优化问题,同时取下层问题的对偶间隙作为惩罚项,构造了一个相应的罚问题,然后提出了一个求解该类二层规划问题的全局优化方法。最后,数值结果表明,所提出的方法是可行的。

In this paper, we consider a nonlinear bilevel programming problem in which the lower level is a linear programming problem. By using the dual theory, the original problem is transformed into a single level optimization program. Then, we construct a penalized problem by using the duality gap of the lower level problem as a penalty parameter. Furthermore, we obtain a global solution of the nonlinear bilevel programming problem. Finally, some numerical results show that the proposed method is feasible.