灾序线性空间中E-Benson真有效解的性质研究
发布时间：2019-03-22 20:34
【摘要】：向量优化问题解的性质研究是向量优化理论与方法研究领域中十分重要的研究方向之一.目前为止,一般拓扑线性空间中向量优化问题解的性质研究已有大量结果.当向量优化问题像空间是一般的实线性空间,即无拓扑结构时,如何利用代数内部和向量闭包等工具研究向量优化问题各类解的性质也已成为十分重要的研究课题.本文主要研究改进集的一些基本性质,特别是利用代数内部和向量闭包等研究了一般实线性空间中E-Benson真有效解的一些性质,并讨论它们的一些特殊情形.第一章主要给出了向量优化问题的一些研究背景及其在各类解的性质研究方面的一些主要研究进展.第二章主要研究了改进集的一些拓扑性质.这些结果是对凸集情况下一些经典结果的改进与推广第三章主要基于拓扑线性空间中的E-Benson真有效解的思想,利用代数内部和向量闭包提出了一般实线性空间中向量优化问题的E-Benson真有效解概念.进而在邻近E-次似凸性假设条件下建立了集值向量优化问题E-Benson真有效解的的线性标量化定理、拉格朗日乘子定理、鞍点定理和对偶性结果.第四章主要讨论了第三章建立的主要结果的一些特殊情形.建立了(C ∈)-真有效解的线性标量化定理、拉格朗日乘子定理、鞍点定理和对偶定理.
[Abstract]:The research on the properties of the solution of vector optimization problem is one of the most important research directions in the field of vector optimization theory and method. Up to now, a large number of results have been obtained on the properties of solutions to vector optimization problems in general topological linear spaces. When the vector optimization problem image space is a general real linear space, that is, no topology structure, how to use the algebraic interior and vector closure tools to study the properties of all kinds of solutions of vector optimization problem has become a very important research topic. In this paper, we mainly study some basic properties of improved sets, especially some properties of E-Benson proper efficient solutions in general real linear spaces by using algebraic interior and vector closures, and discuss some special cases of them. In the first chapter, some research background of vector optimization problem and its main research progress on the properties of all kinds of solutions are given. In the second chapter, we mainly study some topological properties of the improved set. These results are improvements and generalizations of some classical results in the case of convex sets. Chapter 3 is mainly based on the idea of E-Benson proper efficient solutions in topological linear spaces. The concept of E-Benson proper efficient solution for vector optimization problems in general real linear spaces is proposed by using algebraic interior and vector closures. Furthermore, the linear scaling theorem, Lagrangian multiplier theorem, saddle point theorem and duality result of E-Benson proper efficient solution for set-valued vector optimization problems are established under the assumption of adjacent E-subconvexity. The fourth chapter mainly discusses some special cases of the main results established in Chapter 3. The linear scaling theorem, Lagrange multiplier theorem, saddle point theorem and duality theorem of (C 鈭，
本文编号：2445899
[Abstract]:The research on the properties of the solution of vector optimization problem is one of the most important research directions in the field of vector optimization theory and method. Up to now, a large number of results have been obtained on the properties of solutions to vector optimization problems in general topological linear spaces. When the vector optimization problem image space is a general real linear space, that is, no topology structure, how to use the algebraic interior and vector closure tools to study the properties of all kinds of solutions of vector optimization problem has become a very important research topic. In this paper, we mainly study some basic properties of improved sets, especially some properties of E-Benson proper efficient solutions in general real linear spaces by using algebraic interior and vector closures, and discuss some special cases of them. In the first chapter, some research background of vector optimization problem and its main research progress on the properties of all kinds of solutions are given. In the second chapter, we mainly study some topological properties of the improved set. These results are improvements and generalizations of some classical results in the case of convex sets. Chapter 3 is mainly based on the idea of E-Benson proper efficient solutions in topological linear spaces. The concept of E-Benson proper efficient solution for vector optimization problems in general real linear spaces is proposed by using algebraic interior and vector closures. Furthermore, the linear scaling theorem, Lagrangian multiplier theorem, saddle point theorem and duality result of E-Benson proper efficient solution for set-valued vector optimization problems are established under the assumption of adjacent E-subconvexity. The fourth chapter mainly discusses some special cases of the main results established in Chapter 3. The linear scaling theorem, Lagrange multiplier theorem, saddle point theorem and duality theorem of (C 鈭，
本文编号：2445899
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