集值优化强有效解的广义二阶锥方向导数刻画  

Characterizations on strongly efficient solutions of set-valued optimization with generalized second-order cone-directed derivatives

作　　者：徐义红[1] 孙鑫[1] 汪涛[1] 

机构地区：[1]南昌大学数学系,南昌330031

出　　处：《运筹学学报》2013年第4期80-86,共7页Operations Research Transactions

基　　金：国家自然科学基金(No.61175127);江西省自然科学基金(No.20122BAB201003);江西省教育厅科技基金(No.GJJ12010)

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Henig扩张锥和基泛函的性质,利用广义二阶锥方向相依导数,得到受约束于集值映射的优化问题,取得强有效元的二阶最优性必要条件.当目标函数为近似锥-次类凸映射时,利用强有效点的标量化定理,得到集值优化问题,取得强有效元的二阶充分条件.The strong efficiency for set-valued optimization is considered in real normed spaces. With the help of the properties of Henig dilating cone and base functional, by applying generalized second-order cone-directed contingent derivates, a second-order optimality necessary condition is established for a pair to be a strongly efficient element of set-valued optimization whose constraint condition is determined by a set-valued mapping. When objective function is nearly cone-subconvexlike, with the scalarization theorem for a strongly efficient point an a pair to be a strongly efficient element optimality sufficient condition is also derived for of set-valued optimization.

关 键 词：强有效性 广义二阶锥方向相依导数 集值优化 

分 类 号：O221[理学—运筹学与控制论]