共轭对偶上的间隙函数  

A Study of Gap Functions on Conjugate dual

作　　者：李楚群 冯世强[2] LI Chuqun;FENG Shiqiang(School of Mathematics and Computer Science, Chongqing Normal University Foreign Trade and Business College, Chongqing 401520, China;School of Mathematics and Computer Science, Xihua Normal University, Nanchong 637009, China)

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,重庆合川401520 [2]西华师范大学数学与信息学院,四川南充637009

出　　处：《钦州学院学报》2018年第3期25-27,共3页Journal of Qinzhou University

基　　金：四川省教育厅自然科学一般项目:向量值优化问题与向量变分不等式解的关系研究(14ZB0142);不连续治疗策略下传染病模型的动力学研究(18ZB0581);西华师范大学英才基金项目:传染病模型的动力学性质及最优控制(17YC373)

摘　　要：通过介绍一类优化问题的原始问题和对偶问题,引入了混合逆变分不等式(简称IMVI)的三种对偶问题,即Lagrange对偶、Fenchel对偶和Fenchel-Lagrange对偶。在一定的条件下分别构造了三种对偶问题的间隙函数,并得到了该间隙函数都是凸的。In this paper, a kind of optimization problem of primal problem and dual problem is analyzed. Three dual problems, namely Lagrange duality and Fenchel duality, Fenchel-Lagrange duality, are introduced for mixed contravariant inequalities（IMVI）. The gap function for the three dual problems is proposed under certain conditions. And it＇s further proved that the gap function is convex under some conditions.

关 键 词：混合逆变分不等式 LAGRANGE对偶 Fenchel对偶 Fenchel—Lagrange对偶 间隙函数 凸函数 

分 类 号：O177.91[理学—数学]