集值映射的Set-Benson次梯度及其应用

Set-Benson-subgradient for Set-valued Map and Its Applications

引进集值映射的Set-Benson次梯度,通过一个具体例子说明了它与现有文献中的Benson次梯度的关系。利用集值映射的Hahn-Banach定理证明了Set-Benson次梯度的存在性定理。作为应用,给出了用它刻画集值优化问题取得Benson真有效元的充分条件。

The Set-Benson-subgradient for set-valued map was introduced, an example was given to demonstrate the relationship between Set-Benson-subgradient and Benson-subgradient. Its existence theorem was given by the Hahn-Banach Theorem for set-valued map. As an application, sufficient condition was established for set-valued op- timization problem to attain Benson properly efficient elements.