集值映射向量优化问题的精确罚函数镇定性和稳定性（英文）

Calmness, Stability and Exact Penalty Function for Vector Optimization Problems of Set-Valued Maps

精确罚函数理论中镇定性和稳定性是非常重要的条件,因为它们是判断精确罚函数的充分必要条件,本文基于集值映射向量优化问题的锥弱有效解,提出它们的镇定性和稳定性概念,并讨论它们的性质,证明在这些概念下集值向量优化问题的罚函数精确性.

Calmness and stability are very important conditions in the theory of exact penalty function because they are sufficient conditions for the exactness of the penalty function. In this paper, based on the cone-weakly efficient solution to vector optimization problem（VOP for short） of set-valued maps, new concepts of calmness and stability are presented and their properties are discussed. We prove that the penalty function of the VOP with set-valued maps is exact under these concepts.