一类广义不变凸函数和向量变分不等式  

A Class of Generalized Invex Functions and Vector Variational Inequalities

作　　者：李茹[1] 余国林[1] 刘伟[1] 刘三阳[2] Li Ru;Yu Guolin;Liu Wei;Liu Sanyang(Institute of Applied Mathematics, geifang University of Nationalities Yinchuan, Ningzia 750021;College of Science, Xidian University, Xi＇an 710071)

机构地区：[1]北方民族大学应用数学研究所,银川750021 [2]西安电子科技大学理学院,西安710071

出　　处：《数学物理学报（A辑）》2017年第6期1029-1039,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(11361001);宁夏自然科学基金(NZ14101)~~

摘　　要：首先在函数不变凸性的基础上,引进了一类广义不变凸函数,称之为(α,ρ,η)-不变凸函数,并给出实例说明了这类广义凸函数的存在性.其次,在(α,ρ,η)-不变凸性假设下,研究了Stampacchia型和Minty型向量变分不等式与多目标规划解之间的关系.最后,利用KKM定理讨论了向量变分不等式解的存在性问题.In this paper, a new kind of generalized invex functions, termed （α,ρ,η）-invex function, is introduced, and some examples are proposed to illustrate its existence. Under the assumption of （α,ρ,η）-invexity, it presents the close relationship between variational-like inequality and multi-objective programming. By using KKM theorem, the existence results are established for vector variational-like inequalities.

关 键 词：向量变分不等式 多目标规划 不变凸函数 KKM定理 

分 类 号：O221[理学—运筹学与控制论]