一个解变分不等式问题的非单调Broyden-like算法  

A Nonmonotone Broyden-like Algorithm for Variational Inequality Problem

作　　者：丁小妹 王平 DING Xiaomei;WANG Ping(Department of Mathematics and Computational Science,Wuyi University,Wuyishan,Fujian 354300,China)

机构地区：[1]武夷学院数学与计算机学院

出　　处：《闽江学院学报》2019年第5期16-23,共8页Journal of Minjiang University

基　　金：福建省自然科学基金(2016J01005);福建省教育厅中青年教师教育科研项目(JA15525,JA15522)

摘　　要：利用Fischer-Burmeister函数,通过引入光滑参数,构造一个新的光滑逼近函数,将变分不等式问题等价转化为方程组问题,建立了解该方程组问题的非单调Broyden-like算法,从而得到了原问题的解,并证明了算法的全局收敛性和一定条件下的局部超线性/二次收敛性。In the paper,by using the Fischer-Burmeister function and introducing smooth parameters,a new smooth approximation function is constructed.And the variational inequality problem is transformed into system of equations.The nonmonotone Broyden-like method for solving this system of equations is established.Thus,the solution of the original problem is obtained.The global and local superlinear/quadratic convergence under certain conditions is proved.

关 键 词：变分不等式问题 全局收敛 非单调线搜索 Broyden-like算法 超线性收敛 

分 类 号：O224.2[理学—运筹学与控制论]