﻿ 非线性方程组问题的一个三项共轭梯度算法 A Three-Term Conjugate Gradient Algorithm for Nonlinear Equations Problems

Operations Research and Fuzziology
Vol.07 No.01(2017), Article ID:19808,6 pages
10.12677/ORF.2017.71004

A Three-Term Conjugate Gradient Algorithm for Nonlinear Equations Problems

Linghua Huang

School of Information and Statistics, Guangxi University of Finance and Economics, Nanning Guangxi

Received: Feb. 6th, 2017; accepted: Feb. 21st, 2017; published: Feb. 24th, 2017

ABSTRACT

This paper designs a three-term conjugate gradient algorithm for nonlinear equations problems and the proposed algorithm has four advantages: (1) the sufficient descent property is satisfied for the search direction; (2) the trust region feature holds for the direction too; (3) the global convergence of the proposed algorithm is possessed; (4) the new algorithm can successfully solve nonlinear equations problems with 1000 dimensions.

Keywords:Nonlinear Equations Problems, Three-Term Conjugate Gradient, Global Convergence

1. 引言

(1.1)

(1.2)

(1.3)

2. 公式和算法

(2.1)

(2.2)

(2.3)

3. 信赖域特点、充分下降性以及全局收敛性

(3.1)

(3.2)

，则(3.2)式的左边成立。关于(3.2)的右边不等式，需要再次利用(2.1)来获得，具体如下

(ii)满足Lipschitz条件，也就是

4. 数值实验

Table 1. Problems name

Table 2. Numerical results

A Three-Term Conjugate Gradient Algorithm for Nonlinear Equations Problems[J]. 运筹与模糊学, 2017, 07(01): 31-36. http://dx.doi.org/10.12677/ORF.2017.71004

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