災序線性空間中E-Benson真有效解的性質研究
發(fā)布時間：2019-03-22 20:34
【摘要】：向量優(yōu)化問題解的性質研究是向量優(yōu)化理論與方法研究領域中十分重要的研究方向之一.目前為止,一般拓撲線性空間中向量優(yōu)化問題解的性質研究已有大量結果.當向量優(yōu)化問題像空間是一般的實線性空間,即無拓撲結構時,如何利用代數內部和向量閉包等工具研究向量優(yōu)化問題各類解的性質也已成為十分重要的研究課題.本文主要研究改進集的一些基本性質,特別是利用代數內部和向量閉包等研究了一般實線性空間中E-Benson真有效解的一些性質,并討論它們的一些特殊情形.第一章主要給出了向量優(yōu)化問題的一些研究背景及其在各類解的性質研究方面的一些主要研究進展.第二章主要研究了改進集的一些拓撲性質.這些結果是對凸集情況下一些經典結果的改進與推廣第三章主要基于拓撲線性空間中的E-Benson真有效解的思想,利用代數內部和向量閉包提出了一般實線性空間中向量優(yōu)化問題的E-Benson真有效解概念.進而在鄰近E-次似凸性假設條件下建立了集值向量優(yōu)化問題E-Benson真有效解的的線性標量化定理、拉格朗日乘子定理、鞍點定理和對偶性結果.第四章主要討論了第三章建立的主要結果的一些特殊情形.建立了(C ∈)-真有效解的線性標量化定理、拉格朗日乘子定理、鞍點定理和對偶定理.
[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，
本文編號：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，
本文編號：2445899
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