一般混合变分不等式的新间隙函数  

New Gap Functions for General Mixed Variational Inequalities

作　　者：赖学李 夏福全[1] LAI Xueli;XIA Fuquan(College of Mathematical Science,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]四川师范大学数学科学学院

出　　处：《四川师范大学学报（自然科学版）》2019年第6期746-752,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：教育部科学技术重点项目(212147)

摘　　要：主要研究具有凸约束的一般混合变分不等式问题的间隙函数.首先给出间隙函数的概念,研究新间隙函数的连续性和可微性.然后利用新的间隙函数将一般混合变分不等式问题转化为具有线性近似约束的二次规划问题,并证明了目标变分不等式和具有线性近似约束的二次规划问题具有相同的解.In this paper,the gap function of a general mixed variational inequality with convex constraints is studied.First,the concept of gap functions and the properties of new gap functions are given.Then we use the new gap function to transform the general mixed variational inequality problem into a quadratic programming problem with linear approximation constraints,and further into a linear quadratic constrained two degree programming problem.It is proved that the objective variational inequality and the two order programming problem with linear approximation constraints have the same solution.

关 键 词：一般混合变分不等式 KKT条件 间隙函数 

分 类 号：O176[理学—数学] O178[理学—基础数学]