二层凸规划的基本性质

Basic Properties of Convex Two-level Programming

本文研究了一类描述二层决策问题的二层数学规划模型。在一定条件下讨论了下层极值函数和上层复合目标函数的凸性和连续性,给出了二层决策问题最优决策的存在条件。

In this paper, a two-level mathematical programming model, which describes a set of two-level decision making problems,is considered. Convexity and continiuty of optimal value function at the lower-level and composite objective function at the upper-level are discussed by using the concept of point-to-set maps. An existence condition of optimal decision making for the two-level decision making problems is given by using the method of recession direction.