高阶广义弱Studniarski上导数及对复合集值优化问题的应用  

Higher-Order Generalized Weak Studniarski Epiderivatives and Applications to Composite Set-Valued Optimization Problems

作　　者：何柳 王其林 张晓艳 唐田 HE LIU;WANG QILIN;ZHANG XIAOYAN;TANG TIAN(College of General Education,Chongqing Vocational and Technical University of Mechatronics,Chongqing 402760,China;College of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,China)

机构地区：[1]重庆机电职业技术大学通识教育学院,重庆402760 [2]重庆交通大学数学与统计学院,重庆400074

出　　处：《应用数学学报》2024年第2期312-332,共21页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(批准号:N0.11971078);重庆市教委科学技术研究重点项目(批准号:KJZD-K202300708);重庆市高校创新研究群体项目(批准号:CXQT21021)资助项目。

摘　　要：本文引入了集值映射不带低阶逼近方向的高阶广义弱Studniarski上导数,并且讨论了该导数的一些性质和运算法则.利用高阶广义弱Studniarski上导数及其性质,建立了复合集值优化问题弱有效解的高阶最优性充分条件和必要条件,并且给出了一些例子来验证所获得的结果.In this paper,we introduce the notion of higher-order generalized weak Studniarski epiderivatives for a set-valued map without lower-order approximating di-rections and obtain chain and sum operation rules of the epiderivative.Then by apply-ing the higher-order epiderivative,we establish the optimality conditions of the weakly efficient solution for unconstrained composite set-valued optimization problems.Some illustrative examples are provided as well.

关 键 词：复合集值优化问题 高阶广义弱Studniarski上导数 高阶最优性条件 弱有效解 

分 类 号：O224[理学—运筹学与控制论]