Optimality Condition for a Class of the Two-level Decision Model with Multiple Objectives
一类二层多目标决策模型的最优性条件

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.