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集值优化问题的高阶最优性条件(借助Studniarski导数)(英文)
引用本文:孙祥凯,李声杰,程莹,赵培.集值优化问题的高阶最优性条件(借助Studniarski导数)(英文)[J].数学进展,2011(4).
作者姓名:孙祥凯  李声杰  程莹  赵培
作者单位:重庆虎溪大学城重庆大学数学与统计学院;苏州大学数学科学学院;
基金项目:partially supported by NSFC(No.10871216); the Fundamental Research Funds for the Central Universities(No.CDJXS10100011)
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.

关 键 词:Studniarski导数  严格局部有效解  高阶最优性条件  集值优化  

Higher-order Optimality Conditions for Set-Valued Optimization via Studniarski Derivatives
SUN Xiangkai,LI Shengjie,CHENG Ying,ZHAO Pei.Higher-order Optimality Conditions for Set-Valued Optimization via Studniarski Derivatives[J].Advances in Mathematics,2011(4).
Authors:SUN Xiangkai  LI Shengjie  CHENG Ying  ZHAO Pei
Institution:SUN Xiangkai~(1,*),LI Shengjie~(1,**),CHENG Ying~(2,***),ZHAO Pei~(1,****) (1.College of Mathematics and Statistics,Chongqing University,Chongqing,401331,P.R.China,2.College of Mathematical Sciences,Suzhou University,Suzhou,Jiangsu,215006,P.R.China)
Abstract:This paper deals with higher-order optimality conditions of a set-valued optimization 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 optimality 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 ...
Keywords:Studniarski derivatives  strict local minimizers  higher-order optimality conditions  set-valued optimization  
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