一种改进的解大规模凸约束非线性方程组的共轭梯度投影算法  

An Improved Conjugate Gradient Projection Algorithm for SolvingLarge-scale Convex Constrained Nonlinear Systems of Equations

作　　者：夏艳 李丹丹 李远飞 XIA Yan;LI Dandan;LI Yuanfei(Department of Applied Mathematics,Guangzhou Huashang College,Guangzhou 511300,China)

机构地区：[1]广州华商学院应用数学系,广东广州511300

出　　处：《云南师范大学学报（自然科学版）》2024年第5期11-16,共6页Journal of Yunnan Normal University:Natural Sciences Edition

基　　金：广西省自然科学基金资助项目(2020GXNSFAA159069);广州华商学院导师制资助项目(2023HSDS38).

摘　　要：为推进大规模凸约束非线性方程组的数值方法研究,设计一个改进的共轭参数,构建了一个具有充分下降性与信赖域特性的搜索方向,结合无导数线搜索方法和投影技术,提出了一种新的无导数共轭梯度投影算法并证明了其全局收敛性.数值结果表明相比同类共轭梯度算法,新算法在求解大规模凸约束非线性方程组时具有高效的求解能力和鲁棒性.To promote the study of numerical methods for large-scale convex constrained nonlinear equations,combing with a derivative-free line search method and projection technique,a novel derivative-free conjugate gradient projection algorithm was proposed by designing an improved conjugate parameter and constructing a new search direction with sufficient descent property and trust region feature.And the global convergence of the new algorithm was also proven.Compared with similar conjugate gradient methods,the numerical results show that the new algorithm is efficient and competitive for large-scale nonlinear equations.

关 键 词：大规模 凸约束 非线性方程组 无导数 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]