集值优化问题Benson真有效解的最优性条件

【作者】 付守贵；

【导师】 旷华武；

【作者基本信息】 贵州大学 ， 基础数学， 2009， 硕士

【摘要】 本文在赋范线性空间中讨论了集值优化问题的Benson真有效性。在近似锥次类凸等条件下,利用集值映射的切导数与凸集分离定理等得到了集值优化问题关于Benson真有效元的Fritz-John型最优性必要条件。然后,在Slater型约束规格下得到了集值优化问题Benson真有效元的Kuhn-Tucker型最优性必要条件;同时,我们给出了一个Benson真有效元的充分条件等。最后,我们讨论了集值优化问题ε-Benson真有效元的导数型最优性必要条件与充分条件。具体内容如下:本文包括四章。第一章对论文的背景作了简要的介绍。第二章是预备知识,介绍了锥、锥凸集值函数、切锥与集值映射的切导数等的相关知识。第三章讨论了集值优化问题Benson真有效解的最优性条件。第四章研究了集值优化问题ε-Benson真有效解的最优性条件。更多还原

【Abstract】 In this paper, the Benson proper efficiency for set-valued optimization problem is discussed in normed linear space. Under the assumption of nearly cone-subconvexlikeness, by using the tangent derivatives of set-valued mapping and the separation theory for convex sets and so on, The Fritz-John type necessary conditions for set-valued optimization problem in the sense of Benson proper efficient elements is obtained. And then, under the Slater type constraint qualification, the Kuhn-tucker type necessary conditions for set-valued optimization problem in the sense of Benson proper efficient elements is established; at the same time, we gain a sufficient conditions for Benson proper efficient elements. Finally, we discuss the derivative type necessary and sufficient conditions for set-valued optimization problem in the sense ofε-Benson proper efficient elements. The main points of this paper is as followes:This paper includes four parts.The first chapter is an introduction; the background of this paper is introduced.In chapter 2, we introduce the knowledge that the paper use, introducing these conception of cone , cone convex set-valued maps , tangent cones , and tangent derivatives of set-valued mapping, etc.In chapter 3, we discuss the optimality conditions of set-valued optimization problem in the sense of Benson proper efficient solution.In chapter 4, we study the optimization conditions ofε- Benson proper efficient solution of set-valued optimization problem.更多还原