求解凸约束非线性方程组的无导数DY投影算法  

Derivative-Free DY Projection Algorithm for Large-Scale Nonlinear Equations with Convex Constraints

作　　者：李丹丹 王松华 LI Dandan;WANG Songhua(Department of Applied Mathematics,Guangzhou Huashang College,Guangzhou 511300,China;School of Mathematics and Statistics,Baise University,Baise 533000,China)

机构地区：[1]广州华商学院应用数学系,广州511300 [2]百色学院数学与统计学院,百色533000

出　　处：《天津科技大学学报》2022年第1期76-80,共5页Journal of Tianjin University of Science & Technology

基　　金：广西自然科学基金资助项目(2020GXNSFAA159069);广东财经大学华商学院校内项目(2021HSDS32)。

摘　　要：在高效线搜索方法产生的步长和投影技术产生的新迭代点的基础上,提出了一类求解带凸约束非线性方程组问题的无导数修正DY共轭梯度投影算法.新算法继承了共轭梯度法和投影技术的良好性质,适合于求解大规模优化问题.在一定的假设下,得到新算法的全局收敛性结论.数值结果表明新算法是有效且稳定的,与其他算法相比更具有竞争性.Based on the fact that a steplength and a new iterative point are determined by the efficient line search approach and the projection technique respectively,in this article we propose a modified derivative-free DY conjugate gradient projection algorithm for restricted nonlinear equations.This novel algorithm inherits the good properties of the conjugate gradient method and projection technique,which is suitable to address large-scale optimization issues.It also achieves global convergence under some reasonable assumptions.Moreover,numerical results demonstrate that it is both promising and stable,as well as more competitive than other algorithms.

关 键 词：非线性方程组 无导数 凸约束 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]