一类非线性二层规划问题的目标罚函数方法

AN OBJECTIVE PENALTY FUNCTION METHOD FOR A CLASS OF 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,文章利用线性规划的对偶理论,将其转化为一个单层优化问题.除了添加下层问题的对偶间隙作为惩罚项外,还通过一个目标罚参数来调整上层问题的目标函数值,进而给出了一个求解此类二层规划问题的目标罚函数方法.最后,数值结果表明,所提出的方法是可行的.

In this paper, we consider a class of nonlinear bilevel programming prob- lem in which the lower level is a linear programming problem. Using the dual theory, the original problem is transformed into a single level optimization problem. It not only appends the duality gap of the lower level problem with a penalty, but also gives an objective penalty parameter to adjust the value of the upper level objective func- tion. Then, we construct an objective penalty function method for such a problem. Finally, some numerical results show that the proposed method is feasible.