解凸约束非线性方程组的修正WYL投影算法  

A Modified WYL Project Algorithm for Nonlinear Equations with Convex Constraint

作　　者：李丹丹 李远飞 LI Dandan;LI Yuanfei(Department of Applied Mathematics,Guangzhou Huashang College,Guangdong 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：《河北师范大学学报（自然科学版）》2022年第5期447-453,共7页Journal of Hebei Normal University：Natural Science

基　　金：国家自然科学基金(61907010);广东财经大学华商学院校内项目(2020HSDS15);广东省普通高校创新团队项目(2020WCXTD008)。

摘　　要：为提高求解凸约束非线性方程组的运算效率,完善数值优化算法体系,在Wei-Yao-Liu共轭梯度投影算法的基础上,构建一个具有充分下降性和信赖域特征的搜索方向,提出一个求解大规模凸约束非线性方程组问题的无导数修正Wei-Yao-Liu共轭梯度投影算法.在一定的假设下,分析新算法的全局收敛性质.试验结果表明新算法是有效的,相比于同类算法具有较强的竞争力,且适合于求解大规模优化问题.To raise the operating efficiency of nonlinear equations with convex constraint and improve the numerical optimization algorithm system, a search direction possessing the properties of sufficient descent and trust region is constructed based on Wei-Yao-Liu conjugate gradient project algorithm.A modified Wei-Yao-Liu conjugate gradient project algorithm with derivative-free is developed for a large-scale nonlinear equations with convex constraint.What′s more, the global convergence of the new algorithm is analyzed under some certain assumptions.Lastly, experiment results show that the new algorithm is efficient, more competitive than similar algorithms and quietly suitable to solve a large-scale optimization problem.

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]