修正PRP共轭梯度方法求解无约束最优化问题

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  • 1. 巴音郭楞职业技术学院公共教育学院, 新疆库尔勒 841000
张慧玲  E-mail: zhl02061146@126.com

收稿日期: 2020-09-02

  网络出版日期: 2022-05-27

Modified PRP conjugate gradient method for unconstrained optimization

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  • 1. School of Public Education, Bayingol Vocational and Technical College, Korla 841000, Xinjiang, China

Received date: 2020-09-02

  Online published: 2022-05-27

摘要

基于著名的PRP共轭梯度方法,利用CG_DESCENT共轭梯度方法的结构,本文提出了一种求解大规模无约束最优化问题的修正PRP共轭梯度方法。该方法在每一步迭代中均能够产生一个充分下降的搜索方向,且独立于任何线搜索条件。在标准Wolfe线搜索条件下,证明了修正PRP共轭梯度方法的全局收敛性和线性收敛速度。数值结果展示了修正PRP方法对给定的测试问题是非常有效的。

本文引用格式

张慧玲, 赛·闹尔再, 吴晓云 . 修正PRP共轭梯度方法求解无约束最优化问题[J]. 运筹学学报, 2022 , 26(2) : 64 -72 . DOI: 10.15960/j.cnki.issn.1007-6093.2022.02.006

Abstract

Based on the PRP conjugate gradient method, we propose an efficient modified PRP conjugate gradient method for solving large-scaled unconstrained optimization problems by using the structure of the CG_DESCENT conjugate gradient method. The proposed method generates a sufficient descent direction at each iteration, which is independent of any line search. Its global convergence and linear convergence rate are established under standard Wolfe line search. The numerical results show that the proposed methods is effective for the given test problems.

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