A subspace minimization conjugate gradient method based on conic model for unconstrained optimization

  • Yufei Li
  • Zexian LiuEmail author
  • Hongwei Liu


In this paper, we present a new conjugate gradient method, in which the search direction is computed by minimizing a selected approximate model in a two-dimensional subspace. That is, if the objective function is not close to a quadratic, the search direction is generated by a conic model. Otherwise, a quadratic model is considered. The direction of the proposed method is proved to possess the sufficient descent property. With the modified nonmonotone line search, we establish a global convergence of the proposed method under appropriate assumptions. R-linear convergence of the proposed method is also analyzed. Numerical results using two different test function collections show that the proposed algorithm is efficient.


Conjugate gradient method Conic model Subspace minimization Nonmonotone line search Global convergence 

Mathematics Subject Classification

90C30 90C06 65K05 



We would like to thank the anonymous referees for their useful suggestions and comments. We also would like to thank Professor Dai, Y. H. and Dr. Kou, C. X. for their CGOPT code, and thank Professor Hager, W. W. and Zhang, H. C. for their CG DESCENT (5.3) code. This research is supported by National Science Foundation of China (No. 11461021) and Shaanxi Science Foundation (No. 2017JM1014).


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXidian UniversityXi’anChina
  2. 2.School of Mathematics and Computer ScienceHezhou UniversityHezhouChina

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