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Volume 34, Issue 4
A Retrospective Trust Region Algorithm with Trust Region Converging to Zero

Jinyan Fan, Jianyu Pan & Hongyan Song

DOI: 10.4208/jcm.1601-m2015-0399

J. Comp. Math., 34 (2016), pp. 421-436.

Published online: 2016-08

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  • Abstract

We propose a retrospective trust region algorithm with the trust region converging to zero for the unconstrained optimization problem. Unlike traditional trust region algorithms, the algorithm updates the trust region radius according to the retrospective ratio, which uses the most recent model information. We show that the algorithm preserves the global convergence of traditional trust region algorithms. The superlinear convergence is also proved under some suitable conditions.

  • Keywords

Retrospective trust region algorithm, Unconstrained optimization, Superlinear convergence.

  • AMS Subject Headings

65K05, 65K10, 90C26, 90C30.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

jyfan@sjtu.edu.cn (Jinyan Fan)

jypan@math.ecnu.edu.cn (Jianyu Pan)

  • BibTex
  • RIS
  • TXT
@Article{JCM-34-421, author = {Fan , JinyanPan , Jianyu and Song , Hongyan}, title = {A Retrospective Trust Region Algorithm with Trust Region Converging to Zero}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {4}, pages = {421--436}, abstract = {

We propose a retrospective trust region algorithm with the trust region converging to zero for the unconstrained optimization problem. Unlike traditional trust region algorithms, the algorithm updates the trust region radius according to the retrospective ratio, which uses the most recent model information. We show that the algorithm preserves the global convergence of traditional trust region algorithms. The superlinear convergence is also proved under some suitable conditions.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1601-m2015-0399}, url = {http://global-sci.org/intro/article_detail/jcm/9804.html} }
TY - JOUR T1 - A Retrospective Trust Region Algorithm with Trust Region Converging to Zero AU - Fan , Jinyan AU - Pan , Jianyu AU - Song , Hongyan JO - Journal of Computational Mathematics VL - 4 SP - 421 EP - 436 PY - 2016 DA - 2016/08 SN - 34 DO - http://doi.org/10.4208/jcm.1601-m2015-0399 UR - https://global-sci.org/intro/article_detail/jcm/9804.html KW - Retrospective trust region algorithm, Unconstrained optimization, Superlinear convergence. AB -

We propose a retrospective trust region algorithm with the trust region converging to zero for the unconstrained optimization problem. Unlike traditional trust region algorithms, the algorithm updates the trust region radius according to the retrospective ratio, which uses the most recent model information. We show that the algorithm preserves the global convergence of traditional trust region algorithms. The superlinear convergence is also proved under some suitable conditions.

Fan , JinyanPan , Jianyu and Song , Hongyan. (2016). A Retrospective Trust Region Algorithm with Trust Region Converging to Zero. Journal of Computational Mathematics. 34 (4). 421-436. doi:10.4208/jcm.1601-m2015-0399
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