【作者】 李敏；

【导师】 徐义红；

【作者基本信息】 南昌大学 ， 运筹学与控制论， 2016， 硕士

【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.提出集值映射的ε-超次梯度概念.在某种假设下,利用凸集分离定理得到ε-超次梯度的存在性定理.给出一个具体例子解释主要结果.在下径向切锥的基础上引进了集值映射下径向切导数的概念.通过此概念,建立了一些重要的性质.在目标函数和约束函数分开的前提下,建立了集值优化问题全局真有效元的优化必要条件.更多还原

【Abstract】 The concept of α- order nearly conε-arcwise connected set-valued mapping is introduced. An example is given to illustrate that the α- order nearly conε-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 conε-arcwise connected, for weakly efficient elements optimality sufficient and necessary conditions are also established.The concept of ε- super subgradient for a set-valued map is introduced. Under certain hypothesis, by applying separation theorem for convex sets, the existence theorem for an ε- super subgradient is obtained. An example is given to illustrate the main result.The concept of lower radial contingent derivative for set-valued map is introduced with help of lower radial contingent cone. By using this concept, some important properties are presented. An optimality necessary condition for a point pair to be a global proper efficient element of set-valued optimization problem is established where objective function and constraint function are separated.更多还原