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Volume 32, Issue 4
A New Nonmonotone Trust Region Algorithm for Solving Unconstrained Optimization Problems

Jinghui Liu & Changfeng Ma

DOI: 10.4208/jcm.1401-m3975

J. Comp. Math., 32 (2014), pp. 476-490.

Published online: 2014-08

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  • Abstract

Based on the nonmonotone line search technique proposed by Gu and Mo (Appl. Math. Comput. 55, (2008) pp. 2158-2172), a new nonmonotone trust region algorithm is proposed for solving unconstrained optimization problems in this paper. The new algorithm is developed by resetting the ratio $ρ_k$ for evaluating the trial step $d_k$ whenever acceptable. The global and superlinear convergence of the algorithm are proved under suitable conditions. Numerical results show that the new algorithm is effective for solving unconstrained optimization problems.

  • Keywords

Unconstrained optimization problems, nonmonotone trust region method, global convergence, superlinear convergence.

  • AMS Subject Headings

90C30.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-32-476, author = {Jinghui Liu and Changfeng Ma}, title = {A New Nonmonotone Trust Region Algorithm for Solving Unconstrained Optimization Problems}, journal = {Journal of Computational Mathematics}, year = {2014}, volume = {32}, number = {4}, pages = {476--490}, abstract = {

Based on the nonmonotone line search technique proposed by Gu and Mo (Appl. Math. Comput. 55, (2008) pp. 2158-2172), a new nonmonotone trust region algorithm is proposed for solving unconstrained optimization problems in this paper. The new algorithm is developed by resetting the ratio $ρ_k$ for evaluating the trial step $d_k$ whenever acceptable. The global and superlinear convergence of the algorithm are proved under suitable conditions. Numerical results show that the new algorithm is effective for solving unconstrained optimization problems.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1401-m3975}, url = {http://global-sci.org/intro/article_detail/jcm/9898.html} }
TY - JOUR T1 - A New Nonmonotone Trust Region Algorithm for Solving Unconstrained Optimization Problems AU - Jinghui Liu & Changfeng Ma JO - Journal of Computational Mathematics VL - 4 SP - 476 EP - 490 PY - 2014 DA - 2014/08 SN - 32 DO - http://doi.org/10.4208/jcm.1401-m3975 UR - https://global-sci.org/intro/article_detail/jcm/9898.html KW - Unconstrained optimization problems, nonmonotone trust region method, global convergence, superlinear convergence. AB -

Based on the nonmonotone line search technique proposed by Gu and Mo (Appl. Math. Comput. 55, (2008) pp. 2158-2172), a new nonmonotone trust region algorithm is proposed for solving unconstrained optimization problems in this paper. The new algorithm is developed by resetting the ratio $ρ_k$ for evaluating the trial step $d_k$ whenever acceptable. The global and superlinear convergence of the algorithm are proved under suitable conditions. Numerical results show that the new algorithm is effective for solving unconstrained optimization problems.

Jinghui Liu and Changfeng Ma. (2014). A New Nonmonotone Trust Region Algorithm for Solving Unconstrained Optimization Problems. Journal of Computational Mathematics. 32 (4). 476-490. doi:10.4208/jcm.1401-m3975
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