向量优化问题弱E-有效解的代数性质（英文）  

Algebraic Characterizations of Weakly E-efficient Solutions for Vector Optimization Problems

作　　者：林安[1] 朱巧[2] 赵克全[2] 

机构地区：[1]重庆师范大学涉外商贸学院数学与计算机学院,重庆401520 [2]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2017年第4期17-23,共7页Journal of Chongqing Normal University:Natural Science

基　　金：The National Natural Science Foundation of China(No.11431004;No.11671062;No.11271391);The Foundation and Frontier Project of Chongqing(No.cstc2015jcyjA00027);the Education Committee Research Foundation of Chongqing(No.KJ1500303)~~

摘　　要：【目的】研究一类集值向量优化问题。【方法】利用代数内部这一概念,建立基于改进集而定义的集值映射邻近E-次似凸性的择一性定理,进而应用该定理来研究集值向量优化问题。【结果】给出了基于代数内部和改进集而定义的弱E-有效解的线性标量化结果和拉格朗日乘子定理,同时也给出了一些例子并对主要结果进行了解释。【结论】主要结果是对最近一些文献中相应结果的改进与推广。[Purposes]A class of vector optimization problems with set-valued maps are studied. [Methods]By means of the basic notion of algebraic interior, an alternative theorem with nearly E-subconvexlikeness of set-valued maps is established via improvement set and as applications, a class of vector optimization problems with set-valued maps are further considered. [Findings] Linear scalarization theorem and Lagrange multiplier theorem are given for weakly E-efficient solutions via improvement set and algebraic interior. Some examples also are presented to illustrate the main results. [Conclusions] The main results improve and generalize some corresponding results in the literatures.

关 键 词：集值向量优化问题 改进集 代数内部 邻近E-次似凸性 弱E-有效解 标量化 

分 类 号：O221.6[理学—运筹学与控制论]