摘要
在Hilbert空间中,考虑上层约束为有限个不等式,下层为锥约束的一类悲观二层规划问题。首先利用上层问题的极大化最优值函数和下层问题的极小化最优值函数将原问题化为单层约束优化问题,在适当的假设条件下,结合上层极大化最优值函数的次微分估计和下层极小化最优值函数方向导数上下界的性质得到了原问题一阶必要最优性条件的详细刻画。
In this paper,we investigate a class of pessimistic bilevel programming problem,where the upper-level problem consists of a finite number of inequalities constraints and the lower-level problem is a cone constrained optimization problem. Firstly,using the maximization optimal value function of the upper-level problem and the minimization optimal value function of the lower-level problem,we translate the original problem into a single-level constrained optimization problem. Under some suitable assumptions,considering the subdifferential estimate of the maximization optimal value function and the properties of the upper and lower bound of the minimization optimal value functions directional derivative,we obtain the detailed first-order necessary optimality conditions for the original problem.
出处
《山东大学学报（理学版）》
CAS
CSCD
北大核心
2016年第3期44-50,共7页
Journal of Shandong University(Natural Science)
基金
安徽省高校自然科学基金重点资助项目(KJ2014A139)
关键词
悲观二层规划问题
一阶必要最优性条件
Robinson约束规范
最优值函数方法
方向导数
约束非退化条件
pessimistic bilevel programming problem
first-order necessary optimality conditions
Robinson constraint qualification
optimal value function method
directional derivatives
constraint nondegeneracy condition
