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Volume 33, Issue 2
A Direct Search Frame-Based Adaptive Barzilai-Borwein Method

Xiaowei Fang & Qin Ni

DOI: 10.4208/jcm.1411-m4519

J. Comp. Math., 33 (2015), pp. 179-190.

Published online: 2015-04

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  • Abstract

This paper proposes a direct search frame-based adaptive Barzilai-Borwein method for unconstrained minimization. The method is based on the framework of frame-based algorithms proposed by Coope and Price, but we use the strategy of ABB method and the rotational minimal positive basis to reduce the computation work at each iteration. Under some mild assumptions, the convergence of this approach will be established. Through five hundred and twenty numerical tests using the CUTEr test problem library, we show that the proposed method is promising.

  • Keywords

Direct search, Rotational minimal positive basis, Adaptive Barzilai-Borwein method.

  • AMS Subject Headings

90C56, 90C30, 65K05.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

fangxiaowei@163.com (Xiaowei Fang)

niqfs@nuaa.edu.cn (Qin Ni)

  • BibTex
  • RIS
  • TXT
@Article{JCM-33-179, author = {Fang , Xiaowei and Ni , Qin}, title = {A Direct Search Frame-Based Adaptive Barzilai-Borwein Method}, journal = {Journal of Computational Mathematics}, year = {2015}, volume = {33}, number = {2}, pages = {179--190}, abstract = {

This paper proposes a direct search frame-based adaptive Barzilai-Borwein method for unconstrained minimization. The method is based on the framework of frame-based algorithms proposed by Coope and Price, but we use the strategy of ABB method and the rotational minimal positive basis to reduce the computation work at each iteration. Under some mild assumptions, the convergence of this approach will be established. Through five hundred and twenty numerical tests using the CUTEr test problem library, we show that the proposed method is promising.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1411-m4519}, url = {http://global-sci.org/intro/article_detail/jcm/9835.html} }
TY - JOUR T1 - A Direct Search Frame-Based Adaptive Barzilai-Borwein Method AU - Fang , Xiaowei AU - Ni , Qin JO - Journal of Computational Mathematics VL - 2 SP - 179 EP - 190 PY - 2015 DA - 2015/04 SN - 33 DO - http://doi.org/10.4208/jcm.1411-m4519 UR - https://global-sci.org/intro/article_detail/jcm/9835.html KW - Direct search, Rotational minimal positive basis, Adaptive Barzilai-Borwein method. AB -

This paper proposes a direct search frame-based adaptive Barzilai-Borwein method for unconstrained minimization. The method is based on the framework of frame-based algorithms proposed by Coope and Price, but we use the strategy of ABB method and the rotational minimal positive basis to reduce the computation work at each iteration. Under some mild assumptions, the convergence of this approach will be established. Through five hundred and twenty numerical tests using the CUTEr test problem library, we show that the proposed method is promising.

Fang , Xiaowei and Ni , Qin. (2015). A Direct Search Frame-Based Adaptive Barzilai-Borwein Method. Journal of Computational Mathematics. 33 (2). 179-190. doi:10.4208/jcm.1411-m4519
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