α-阶近似锥-弧连通集值优化弱有效元的最优性条件  

OPTIMALITY CONDITIONS FOR WEAKLY EFFICIENT ELEMENTS OF SET-VALUED OPTIMIZATION WITH α-ORDER NEAR CONE-ARCWISE CONNECTEDNESS

作　　者：徐义红[1] 李敏[1] XU Yihong LI Min(Department of Mathematics, Nanchang University, Nanchang 330031)

机构地区：[1]南昌大学数学系,南昌330031

出　　处：《系统科学与数学》2016年第10期1721-1729,共9页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金资助项目(11461044);江西省自然科学基金项目(20151BAB201027);江西省教育厅科技项目(GJJ12010)资助课题

摘　　要：引进了α-阶近似锥-弧连通集值映射,举例说明了它是锥-弧连通集值映射的真推广.借助Y-切锥引进了广义Y-切上图导数,讨论了它与广义切上图导数的关系.当目标函数为α-阶近似锥-弧连通集值映射时,得到集值优化取得弱有效元的充分和必要条件.The concept of α-order nearly cone-arcwise connected set-valued mapping is introduced. An example is given to illustrate that the α-order nearly cone-arcwise connected set-valued mapping is a proper generalization of the cone arcwise connected set-valued mapping. With the help of Y-contingent cone, generalized Y-contingent epiderivative is introduced, and the relationship between generalized Y-contingent epiderivative and generalized contingent epiderivative is discussed. When objective function is α-order nearly cone-arcwise connected, for weakly efficient elements opti- mality sufficient and necessary conditions are also established.

关 键 词：α-阶近似锥弧连通集值映射 广义Y-切上图导数 弱有效元 

分 类 号：O224[理学—运筹学与控制论]