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.
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.
出处
《数学杂志》
CSCD
北大核心
2012年第6期1069-1074,共6页
Journal of Mathematics
基金
国家青年自然科学基金资助(10901004)
北方民族大学自主科研基金资助(2011)
