求解变分不等式的非单调混合Newton算法  

A Non-monotone Hybrid Newton Method for Solving the Variational Inequality Problems

作　　者：宫恩龙[1] 王宣战 高苗苗 杜小雨 孙清滢 

机构地区：[1]青岛酒店管理职业技术学院,青岛266100 [2]中国石油大学(华东)理学院,青岛266580

出　　处：《工程数学学报》2017年第5期507-516,共10页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(61201455)~~

摘　　要：本文运用广义D-间隙函数可以将变分不等式问题转化为一个无约束最优化问题,即极小化广义D-间隙函数的一般形式gαβ,基于非单调线搜索技术提出一种非单调混合Newton算法,并给出了算法的全局收敛性分析.在适当条件下,证明了算法具有全局二次收敛性.同时在映射F强单调但不需要Lipschitz连续的情况下,为算法提供了一个全局误差界.数值结果表明新算法是有效的.In this paper, the variational inequality problem is transformed as an unconstrained optimization problem through the generalized D-gap function. A non-monotone hybrid Newton method based on Zhang H.C.＇s non-monotone line search technique is proposed for minimizing the general form of the generalized D-gap function. Then, the global convergence property of the algorithm is analyzed. Under some proper conditions, we prove that the algorithm is globally quadratically convergent. Moreover, we obtain a global error bound of the algorithm when the mapping F is strongly monotone without Lipschitz continuous. Numerical results indicate that the new algorithm is efficient.

关 键 词：广义D-间隙函数 非单调线搜索 全局收敛 全局误差界 

分 类 号：O221.2[理学—运筹学与控制论]