摘要
本文研究的是约束集值优化问题的高价最优性条件.首先通过借助集值映射的Stud-niarski导数和严格局部有效性,讨论了集值优化问题的高阶必要条件和充分条件.对于充分条件,初始空间必须是有限维的.其次在初始空间和目标空间是有限维的以及集值映射是m阶稳定的条件下,也得到了此约束集值优化问题的高阶最优性条件.
This paper deals with higher-order optimality conditions of a set-valued optimiza- tion problem（SOP） whose constraint condition is determined by a fixed set. By virtue of Studniarski derivatives of set-valued maps and strict local efficiency, higher-order necessary and sufficient opti- mality conditions for SOP are obtained. For the sufficient conditions, the initial space must be finite dimensional. Higher-order optimality conditions for SOP are also investigated under the conditions that the initial and objective spaces are finite dimensional and the multifunction involved is ruth-order stable.
出处
《数学进展》
CSCD
北大核心
2011年第4期433-440,共8页
Advances in Mathematics（China）
基金
partially supported by NSFC(No.10871216)
the Fundamental Research Funds for the Central Universities(No.CDJXS10100011)
