中文摘要：

本文研究了集值映射的Moreau-Rockafellar型定理的问题.利用集值映射弱次梯度的Moreau-Rockafellar定理,在内部（锥）-凸条件下,获得了集值映射关于全局真有效性的Moreau-Rockafellar型定理结果,推广了集值映射在锥-凸假设下的Moreau-Rockafellar型定理的结果,所得结论深化和丰富了最优化理论的内容.

英文摘要：

This paper deals with the Moreau-Rockfellar theorem for set-valued maps.By using the Moreau-Rockfellar theorem for weak subgradients of the set-valued maps,MoreauRockfellar theorem for globally proper effcient subgradients are established under the assumptions of int-convexity（intcone-convexity）.The conclusion obtained in this note is a generation of Moreau-Rockfellar theorem under the conditions of cone-convexity for set-valued maps,It shows that a globally proper effcient subgradient of the sum of two set-valued maps can be expressed as the sum of two globally proper effcient subgradients of these maps,and these results deepen and enrich the content of optimization theory.