Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2022, Vol. 39 ›› Issue (2): 265-276.doi: 10.3969/j.issn.1005-3085.2022.02.007

Previous Articles     Next Articles

A Modified PRP Type Spectral Conjugate Gradient Method with Sufficient Descent Property

JIAN Jinbao,   SONG Dan,   JIANG Xianzhen   

  1. College of Mathematics and Physics, Guangxi University for Nationalities, Nanning 530006
  • Online:2022-04-15 Published:2022-06-15
  • Contact: X. Jiang. E-mail address: yl2811280@163.com
  • Supported by:
    The National Natural Science Foundation of China (11771383); the Natural Science Foundation of Guangxi Province (2018GXNSFFA281007); the Research Project of Guangxi University for Nationalities (2018KJQD02); the Innovation Project of Guangxi Graduate Education (gxun-chxzs2019034).

Abstract:

A modified PRP type spectral conjugate gradient method with sufficient descent property spectral conjugate gradient method is an important extension of conjugate gradient method. By adjusting the conjugate parameters and spectral parameters, the search direction of the designed algorithm can meet a certain preset condition, such as sufficient descent condition or conjugate condition. The two core tasks of designing spectral parameters and conjugate parameters are spectral conjugate gradient method, which determine the convergence and numerical effect of the method. Based on the PRP method, a modified PRP type conjugate parameter is proposed and a spectral parameter is chosen by sufficient descent conditions, and then a new spectral conjugate gradient method is established. Sufficient descent condition of the new algorithms does not depend on any line search. Under the usual assumptions, using the strong Wolfe line search to generate the step-length, the global convergence of the presented method is proved. By testing 100 numerical experiments, the corresponding performance profiles for the proposed method and other five comparisons are reported, which indicate that the proposed method is effective.

Key words: unconstrained optimization, spectral conjugate gradient method, strong Wolfe line search, global convergence

CLC Number: