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Volume 39, Issue 2
A New Adaptive Subspace Minimization Three-Term Conjugate Gradient Algorithm for Unconstrained Optimization

Keke Zhang, Hongwei Liu & Zexian Liu

DOI: 10.4208/jcm.1907-m2018-0173

J. Comp. Math., 39 (2021), pp. 159-177.

Published online: 2020-11

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  • Abstract

A new adaptive subspace minimization three-term conjugate gradient algorithm with nonmonotone line search is introduced and analyzed in this paper. The search directions are computed by minimizing a quadratic approximation of the objective function on special subspaces, and we also proposed an adaptive rule for choosing different searching directions at each iteration. We obtain a significant conclusion that the each choice of the search directions satisfies the sufficient descent condition. With the used nonmonotone line search, we prove that the new algorithm is globally convergent for general nonlinear functions under some mild assumptions. Numerical experiments show that the proposed algorithm is promising for the given test problem set.

  • Keywords

Conjugate gradient method, Nonmonotone line search, Subspace minimization, Sufficient descent condition, Global convergence.

  • AMS Subject Headings

90C30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

Coco_xidian@163.com (Keke Zhang)

hwliu@mail.xidian.edu.cn (Hongwei Liu)

liuzexian2008@163.com (Zexian Liu)

  • BibTex
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  • TXT
@Article{JCM-39-159, author = {Zhang , KekeLiu , Hongwei and Liu , Zexian}, title = {A New Adaptive Subspace Minimization Three-Term Conjugate Gradient Algorithm for Unconstrained Optimization}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {39}, number = {2}, pages = {159--177}, abstract = {

A new adaptive subspace minimization three-term conjugate gradient algorithm with nonmonotone line search is introduced and analyzed in this paper. The search directions are computed by minimizing a quadratic approximation of the objective function on special subspaces, and we also proposed an adaptive rule for choosing different searching directions at each iteration. We obtain a significant conclusion that the each choice of the search directions satisfies the sufficient descent condition. With the used nonmonotone line search, we prove that the new algorithm is globally convergent for general nonlinear functions under some mild assumptions. Numerical experiments show that the proposed algorithm is promising for the given test problem set.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1907-m2018-0173}, url = {http://global-sci.org/intro/article_detail/jcm/18369.html} }
TY - JOUR T1 - A New Adaptive Subspace Minimization Three-Term Conjugate Gradient Algorithm for Unconstrained Optimization AU - Zhang , Keke AU - Liu , Hongwei AU - Liu , Zexian JO - Journal of Computational Mathematics VL - 2 SP - 159 EP - 177 PY - 2020 DA - 2020/11 SN - 39 DO - http://doi.org/10.4208/jcm.1907-m2018-0173 UR - https://global-sci.org/intro/article_detail/jcm/18369.html KW - Conjugate gradient method, Nonmonotone line search, Subspace minimization, Sufficient descent condition, Global convergence. AB -

A new adaptive subspace minimization three-term conjugate gradient algorithm with nonmonotone line search is introduced and analyzed in this paper. The search directions are computed by minimizing a quadratic approximation of the objective function on special subspaces, and we also proposed an adaptive rule for choosing different searching directions at each iteration. We obtain a significant conclusion that the each choice of the search directions satisfies the sufficient descent condition. With the used nonmonotone line search, we prove that the new algorithm is globally convergent for general nonlinear functions under some mild assumptions. Numerical experiments show that the proposed algorithm is promising for the given test problem set.

Keke Zhang, Hongwei Liu & Zexian Liu. (2020). A New Adaptive Subspace Minimization Three-Term Conjugate Gradient Algorithm for Unconstrained Optimization. Journal of Computational Mathematics. 39 (2). 159-177. doi:10.4208/jcm.1907-m2018-0173
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