无约束线性二层规划问题的区间算法

An Interval Algorithm for Unconstrained Linear Bilevel Programming

利用区间分析研究无约束线性二层规划问题的数值方法。通过建立目标函数的区间扩张和构造无解区域删除检验原则,建立区间算法,证明了算法的收敛性,并进行数值实验,给出数值算例。该算法可以同时求出二层规划的最优值和全部最优解的区间值。算例结果表明该算法是可靠和有效的。

We describe an interval algorithm for a class of unconstrained linear bilevel programming problems.By setting up an interval extension of the objective function and the region deletion test rules,an interval algorithm is established.Numerical experiments are performed for the algorithm and numerical results are presented.The method can get both the optimal value and the interval value of all global solutions.The results show that the algorithm is reliable and efficient.