解变分不等式的简单牛顿法的收敛性  

Convergence of Newton method for solving variational inequalities

作　　者：周彪[1] 李素兰[1] 

机构地区：[1]浙江工业大学理学院,浙江杭州310023

出　　处：《浙江工业大学学报》2016年第4期461-465,共5页Journal of Zhejiang University of Technology

基　　金：国家自然科学基金资助项目(11371325)

摘　　要：牛顿法作为求解变分不等式问题的一个重要方法,它的收敛性一直是各位学者研究的一个核心问题.当变分不等式中的函数F在B(x_0,ρ)内满足γ-条件时,证明了由牛顿法产生的迭代点列是适定的,而且解的序列可以被构造出来的{tn}序列控制收敛到一个变分不等式的最优解.考虑到F在B(x_0,ρ)内满足γ-条件这个区域性条件给进一步的研究带来了困难,因此引入了解析函数,给出了F是解析函数条件下的牛顿法的收敛性结果.数值实验表明算法是有效的.Newton method is an important method for solving the problem of variational inequalities,the convergence of the algorithm has been a core issue for the scholars.When the function F in variational inequalities satisfiesγ-conditions in B(x_0,ρ),it is proved that the iterative dot sequence produced by the Newton method is valid and can be controlled to converge to an optimal solution of the variational inequalities by a sequence{tn},which is constructed out.Taking into account that the regional conditions of the function F satisfies γ-conditions in B(x_0,ρ)makes more difficult for further study,analytic functions is introduced.The convergence of Newton method under the condition that the F is analytic function is given.Numerical experiments show that the algorithm is effective.

关 键 词：牛顿法 变分不等式 Γ-条件 半局部收敛 解析函数 

分 类 号：O224[理学—运筹学与控制论]