基于改进集的带约束集值向量均衡问题的最优性条件  

Optimality Conditions for Set-Valued Vector Equilibrium Problems With Constraints Involving Improvement Sets

作　　者：陈望 周志昂 CHEN Wang;ZHOU Zhiang(School of Sciences,Chongqing University of Technology,Chongqing 400054,P.R.China)

机构地区：[1]重庆理工大学理学院,重庆400054

出　　处：《应用数学和力学》2018年第10期1189-1197,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11431004;11471291);重庆市前沿与应用基础研究计划项目(cstc2015jcyjA00050;cstc2017jcyjBX0055;cstc2015jcyjBX0113)~~

摘　　要：在局部凸空间中,研究了带约束集值向量均衡问题的最优性条件.首先,利用改进集引进了带约束集值向量均衡问题的E-Henig真有效解和E-超有效解的概念.其次,在邻近E-次似凸的假设下,建立了带约束集值向量均衡问题的E-Henig真有效解的充分必要性条件.最后,在邻近E-次似凸的假设下,建立了带约束集值向量均衡问题的E-超有效解的必要性条件.The optimality conditions for set-valued vector equilibrium problems with constraints were investigated in locally convex spaces. Firstly,the concepts of the E-Henig properly efficient solution and the E-super efficient solution to the set-valued vector equilibrium problems with constraints involving improvement sets were introduced. Secondly,under the assumption of the nearly E-subconvexlikeness,the sufficient and necessary conditions for the set-valued vector equilibrium problem with constraints were established in the sense of the E-Henig proper efficiency. Finally,based on the nearly E-subconvexlikeness,the necessary conditions for the set-valued vector equilibrium problem with constraints were obtained in the sense of the E-super efficiency.

关 键 词：改进集 邻近E-次似凸 E-Henig真有效解 E-超有效解 最优性条件 

分 类 号：O221.6[理学—运筹学与控制论]