集值映射上最优值函数的连续性

Continuity of Optimal Value Function on Point-to-Set Maps

给出了集值映射的连续性概念,讨论了集值映射上最优值函数的连续性,给出在不等式约束、等式和不等式约束情况下最优值函数的连续性定理,并针对最优值函数的方向导数给出了一个在新的约束规格条件下,最优值函数的连续性定理.

In the paper,We define a kind of continuous concepts of optimal value function on point-to-set maps and discuss the continuity of optimal value function on point-to-set maps.The theorem on the continuity of optimal value function under the inequality constraint or the equality and inequality constraint is given.The theorem on the continuity of optimal value function for a new regular is also stated.