Hilbert空间中的一类双层规划问题的一阶与二阶最优性条件  

First and Second Order Optimality Conditions of a Class of Bilevel Programming Problems in Hilbert Spaces

作　　者：王韵[1] 张立卫[1] 

机构地区：[1]大连理工大学应用数学系,大连116024

出　　处：《运筹学学报》2008年第3期90-102,共13页Operations Research Transactions

基　　金：国家自然科学基金项目10771026资助

摘　　要：本文考虑Hilbert空间中的,上层为有限个不等式约束,下层是一锥约束参数规划的双层规划问题的最优性条件.首先,利用下层问题最优值函数的方向导数的上下界的性质给出一阶最优性条件.之后,在使下层问题的最优值函数是二阶方向可微的条件下,证明了二阶必要性条件.The optimality conditions of a bilevel programming problem in a Hilbert space are considered, in which the upper problem consists of a finite number of inequalities constrains and the lower problem is a cone constrained parametric programming problem. A set of first-order necessary optimality conditions based on the the upper and lower bounds of directional derivatives of the optimal value function of lower problem are proposed. And under the conditions that the corresponding optimal value function is second order directionally differentiable, a set of second-order necessary conditions are demonstrated.

关 键 词：运筹学 双层规划 一阶最优性条件 二阶最优性条件 Robinson约束规范 约束非退化条件 最优值函数 方向导数 

分 类 号：O177.1[理学—数学] O221[理学—基础数学]