摘要
本文讨论的极小化双层规划是:其第一层中的目标函数是凸的且约束是线性的,其第二层是带有参数的线性规划。本文提出了一种恰当罚函数法,给出了此双层规划具有这种恰当罚函数法的充要条件。与线性双层规划的有关结果相比较,本文的推广是两方面的:其一是目标函数可以为非线性,其二是第一层中的目标函数允许在由两层中的线性约束所刻划的多胞形上为无下界。
For the minimization problem of the two level programming,where the objective function in the first level is convex and the constraints are linear inequalities,and the second level is a linear program with parameters,we propose an exact penalty reformulation.A necessary and sufficient condition is then presented for the two level problem to admit the exact penalty approach.As compared with the corresponding results in the linear bilevel programs,our generalizations are two fold:the objective function in the first level can be nonlinear,and this function is sometimes allowed to be unbounded below over the polyhedron described by the linear constraints in both levels.
出处
《浙江师大学报（自然科学版）》
1999年第3期1-7,共7页
Journal of Zhejiang Normal University(Natoral Sciences)
关键词
双层规划
恰当罚函数
充要条件
线性规划
two level programs
exact penalty function approach
necessary and sufficient condition
