非线性伪单调方程组的谱LS型投影算法

数学物理学报 ›› 2022, Vol. 42 ›› Issue (6): 1886-1897.

非线性伪单调方程组的谱LS型投影算法

张宁(),刘金魁*()

^{重庆三峡学院数学与统计学院重庆 404100}

收稿日期:2022-03-22 出版日期:2022-12-26 发布日期:2022-12-16
通讯作者: 刘金魁 E-mail:zhangning19990405@126.com;liujinkui2006@126.com
作者简介:张宁, E-mail: zhangning19990405@126.com
基金资助:
重庆市自然科学基金(cstc2021jcyj-msxmX0233);重庆三峡学院研究生科研创新项目(YJSKY22058)

Spectral LS-type Projection Algorithm for Solving Nonlinear Pseudo-Monotone Equations

Ning Zhang(),Jinkui Liu*()

^{School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404100}

Received:2022-03-22 Online:2022-12-26 Published:2022-12-16
Contact: Jinkui Liu E-mail:zhangning19990405@126.com;liujinkui2006@126.com
Supported by:
the Chongqing Research Program of Basic Research and Frontier Technology(cstc2021jcyj-msxmX0233);the Chongqing Three Gorges University Graduate Research Innovation Project(YJSKY22058)

摘要/Abstract

摘要：

基于谱梯度法和著名LS共轭梯度法的结构, 该文建立了求解凸约束非线性伪单调方程组问题的谱LS型无导数投影算法.通过构建适当的谱参数, 该算法在每一次迭代中都能保证搜索方向的充分下降性, 并且独立于线搜索条件.在适当的假设条件和经典无导数线搜索条件下, 算法具有全局收敛性.通过数值实验发现, 该算法继承了LS共轭梯度法优秀的计算性能, 并提高了稳定性.

关键词: 非线性方程组, 无导数投影法, 无导数线搜索, 全局收敛

Abstract:

Based on the structures of the spectral gradient method and the famous LS conjugate gradient method, in this paper we establish an spectral LS-type derivative-free projection algorithm to solve nonlinear pseudo-monotone equations with convex constraints. By using the spectral parameter, the proposed method can generate the descent direction in each iterate, which is independent of any line search. Under some usual assumptions, the global convergence of the proposed method is proved by using the classical derivative-free line search condition. Numerical experiments show that the proposed method inherits the excellent computational performance of the LS conjugate gradient method and improves its stability.

Key words: Nonlinear equations, Derivative-free projection method, Derivative-free line search, Global convergence

中图分类号:

O241

张宁,刘金魁. 非线性伪单调方程组的谱LS型投影算法[J]. 数学物理学报, 2022, 42(6): 1886-1897.

Ning Zhang,Jinkui Liu. Spectral LS-type Projection Algorithm for Solving Nonlinear Pseudo-Monotone Equations[J]. Acta mathematica scientia,Series A, 2022, 42(6): 1886-1897.

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