求解非线性方程组的非单调自适应信赖域方法  

A non-monotonous self-adaptive trust region method for solving the system of nonlinear equations

作　　者：唐江花[1] 马昌凤[1,2] 刘宁[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004 [2]福建师范大学数学与计算机科学学院,福建福州350007

出　　处：《合肥工业大学学报（自然科学版）》2011年第5期790-793,共4页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(11071041)

摘　　要：文章将非线性方程组转化为一个非线性优化问题,结合基于函数值平均权重的非单调技术与自适应信赖域方法求解该问题,从而得到原方程组的解,其中信赖域半径的选取充分应用了当前迭代点的二次信息,新的非单调技术减少了算法的计算量;在合适的条件下,证明了算法的全局收敛性,数值试验表明了算法的有效性。In this paper,the system of nonlinear equations is treated as a nonlinear optimization problem.This problem can be solved by the non-monotonous technology and self-adaptive trust region method based on average weight of function values.Thus a solution of the original system is obtained.The proposed algorithm generates automatically a trust region radius by using the second order information of the current iteration point.The new non-monotonous technology can reduce the computation complexity of the algorithm.Under some reasonable conditions,the proposed algorithm is proved to be globally convergent.The numerical results also show the effectiveness of the algorithm.

关 键 词：非线性方程组 非单调技术 信赖域方法 收敛性 

分 类 号：O221[理学—运筹学与控制论]