凸约束非线性方程组的一种无导数投影方法  

A Derivative-Free Projection Method for Solving Nonlinear Equations with Convex Constraints

作　　者：吴晓云[1] 周学良 WU Xiao-yun;ZHOU Xue-liang(School of Public Education, Bayingol Vocational and Technical College, Xinjiang 841000, China;Department of Public Education, Xinjiang Industrial Vocational and Technical College, Urumqi 830022 China)

机构地区：[1]新疆巴音郭楞职业技术学院公共教育学院,新疆库尔勒841000 [2]新疆工业职业技术学院公共教学部,新疆乌鲁木齐830022

出　　处：《数学的实践与认识》2018年第2期119-126,共8页Mathematics in Practice and Theory

摘　　要：推广LCG共轭梯度方法并建立一种求解凸约束非线性单调方程组问题的无导数投影方法．在适当的条件下，证明了方法的全局收敛性．方法不需要任何导数信息，而且继承了共轭梯度方法储存量小的特征，因此它特别适合求解大规模非光滑的非线性单调方程组问题．大量数值结果和比较表明方法是有效的和稳定的．In this paper, a derivative-free projection method is proposed for solving nonlin- ear monotone equations with convex constraints, which is a generalization of LCG conjugate gradient method. Under some suitable conditions, we prove the global convergence of the pro- posed method. The proposed method does not need any derivative information, and inherits the characteristics of the conjugate gradient method, so it is especially suitable for solving the large-scale non-smooth nonlinear monotone equations. A large number of numerical results and comparisons show that the proposed method is effective and stable.

关 键 词：非线性单调方程组 共轭梯度方法 无导数投影方法 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]