解非线性互补问题的非单调非精确Broyden-like算法  

A Nonmonotone Inexact Broyden-like Algorithm for Nonlinear Complementarity Problem

作　　者：丁小妹 王平 马昌凤 DING Xiaomei;WANG Ping;MA Changfeng(Department of Mathematics and Computational Science,Wuyi University,Wuyishan,Fujian,354300,P.R.China;College of Mathematics and Computer Science,Fujian Normal University,Fuzhou,Fujian,350001,P.R.China)

机构地区：[1]武夷学院数学与计算机学院,武夷山福建354300 [2]福建师范大学数学与信息学院,福州福建350001

出　　处：《数学进展》2019年第1期89-98,共10页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.11071041);武夷学院科技类项目(No.XL201309);福建省教育厅中青年教师科研项目(Nos.JA15525;JA15522)

摘　　要：本文通过构造一个新的光滑互补函数,将非线性互补问题等价转换为光滑方程组问题.将非单调线搜索技术与非精确Broyden-like算法相结合,建立了解非线性互补问题的非单调非精确Broyden-like算法.在一定条件下证明了该算法的全局收敛性和局部二次收敛性.数值实验表明该算法对求解非线性互补问题是十分有效的.In this paper,by constructing a new smoothing complementary function,we reformulate nonlinear complementarity problem as a nonlinear smooth system of equations.Combining non-monotonic line search techniques with an inexact Broyden-like algorithm,we establish a nonmonotone inexact Broyden-like algorithm.The global and local quadratic convergence of this method is proved under suitable conditions.Numerical experiments show that the algorithm is effective for solving nonlinear complementarity problems.

关 键 词：互补问题 全局收敛 局部二次收敛 Broyden-like算法 

分 类 号：O242.23[理学—计算数学]