求解非线性单调方程组的一种无导数投影算法  

A Derivative-free Projection Algorithm for Solving Nonlinear Monotone Equations

作　　者：陈香萍[1] 

机构地区：[1]重庆大学城市科技学院,重庆402167

出　　处：《数学的实践与认识》2017年第13期168-175,共8页Mathematics in Practice and Theory

摘　　要：推广了一种修正的CG_DESCENT共轭梯度方法,并建立了一种有效求解非线性单调方程组问题的无导数投影算法.在适当的线搜索条件下,证明了算法的全局收敛性.由于新算法不需要借助任何导数信息,故它适应于求解大规模非光滑的非线性单调方程组问题.大量的数值试验表明,新算法对给定的测试问题是有效的.In this paper, we extend a modified CG_DESCENT conjugate gradient method, and establish an efficient derivative-free projection algorithm for solving nonlinear monotone equations. The global convergence of the proposed algorithm is proved by using appropriate line search. The proposed algorithm has no need for any information of derivative, so it is very suitable for solving nonsmooth nonlinear monotone equations. Numerical results show that the proposed algorithm is very efficient for some given problems.

关 键 词：非线性单调方程组 非线性共轭梯度方法 无导数投影法 全局收敛性 

分 类 号：O241.7[理学—计算数学]