一类二层多目标决策模型的最优性条件

Optimality Condition for a Class of the Two-level Decisi on Model with Multiple Objectives

讨论二层多目标决策模型的最优性条件 ,其中上层集值目标函数由下层偏好最优解的前沿面确定的 .利用集值映射的 Clarke切导数的概念及其性质 ,且假设上层目标函数是可微的 ,给出并证明了该二层多目标决策模型最优解的一阶必要条件 ,所得必要条件由上层目标函数的梯度和下层最优化问题的前沿面的

In this paper, we discuss the two-level decision model with multiple objectives, that the upper-level set-value objective functions are defined by the forward surfaces of the partial-optimal solutions for the lower-level problems of optimization. We gave and proved the first-order necessary condition of the optimal solutions for this two-level decision model with multiple objectives, applying the concept and properties of the Clarke tangent derivative for set-value map, and assuming that the supper-level objective functions are differentiable. The obtained necessary condition is formed by the gradients of the upper-level objective functions and the Clarke tangent derivatives of forward surfaces for the lower-level problems of optimization.