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用于大规模非线性方程的共轭梯度法族

A family of conjugate gradient methods for large-scale nonlinear equations.

作者信息

Feng Dexiang, Sun Min, Wang Xueyong

机构信息

School of Management Sciences, Fudan University, Shanghai, China.

Qufu Normal University, Shandong, 276826 China.

出版信息

J Inequal Appl. 2017;2017(1):236. doi: 10.1186/s13660-017-1510-0. Epub 2017 Sep 22.

DOI:10.1186/s13660-017-1510-0
PMID:28989261
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC5610229/
Abstract

In this paper, we present a family of conjugate gradient projection methods for solving large-scale nonlinear equations. At each iteration, it needs low storage and the subproblem can be easily solved. Compared with the existing solution methods for solving the problem, its global convergence is established without the restriction of the Lipschitz continuity on the underlying mapping. Preliminary numerical results are reported to show the efficiency of the proposed method.

摘要

在本文中，我们提出了一族用于求解大规模非线性方程的共轭梯度投影方法。在每次迭代时，它所需存储量低且子问题易于求解。与求解该问题的现有方法相比，其全局收敛性的建立无需对基础映射有Lipschitz连续性的限制。报告了初步数值结果以展示所提方法的有效性。