云南师范大学学报(自然科学版)2024,Vol.44Issue(5) :11-16.DOI:10.7699/j.ynnu.ns-2024-057

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 Solving Large-scale Convex Constrained Nonlinear Systems of Equations

夏艳 李丹丹 李远飞
云南师范大学学报(自然科学版)2024,Vol.44Issue(5) :11-16.DOI:10.7699/j.ynnu.ns-2024-057

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 Solving Large-scale Convex Constrained Nonlinear Systems of Equations

夏艳 1李丹丹 1李远飞1
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作者信息

  • 1. 广州华商学院应用数学系,广东 广州 511300
  • 折叠

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.

Abstract

To promote the study of numerical methods for large-scale convex constrained nonlinear e-quations,combing with a derivative-free line search method and projection technique,a novel deriva-tive-free conjugate gradient projection algorithm was proposed by designing an improved conjugate pa-rameter and constructing a new search direction with sufficient descent property and trust region fea-ture.And the global convergence of the new algorithm was also proven.Compared with similar conju-gate 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

Key words

Large-scale/Convex constraint/Nonlinear equations/Derivative-free/Global convergence

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基金项目

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)

出版年

2024
云南师范大学学报(自然科学版)
云南师范大学

云南师范大学学报(自然科学版)

CSTPCD
影响因子:0.54
ISSN:1007-9793
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