集值优化问题强有效元的二阶最优性条件  

Second-Order Optimality Conditions for Strong Efficient Element of Set-Valued Optimization

作　　者：孙鑫[1] 徐义红[1] 汪涛[1] 

机构地区：[1]南昌大学数学系,南昌330031

出　　处：《吉林大学学报（理学版）》2011年第5期861-864,共4页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10461007);江西省自然科学基金(批准号:2009GZS0021);江西省教育厅科技项目(批准号:GJJ09069)

摘　　要：在实赋范线性空间中考虑集值优化问题的强有效性,借助集值映射的二阶切导数,利用基泛函及强有效元的性质,给出了目标函数为近似锥-次类凸时无约束集值优化问题的二阶导数型最优性的必要条件,并在锥-凸假设下给出了充分条件.The strong efficiency of set-valued optimization in real normed spaces was solved by applying the second-order contingent derivatives,the properties of basic functional and strong efficient element.The second-order necessary optimality condition of unconstrained set-valued optimization was given for the objective function being nearly cone-subconvexlike,and sufficient condition was presented under cone-convexity hypothesis.

关 键 词：集值优化 二阶切导数 强有效元 

分 类 号：O224[理学—运筹学与控制论]