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Volume 19, Issue 3
Curvilinear Paths and Trust Region Methods with Nonmonotonic Back Tracking Technique for Unconstrained Optimization

De-Tong Zhu

J. Comp. Math., 19 (2001), pp. 241-258.

Published online: 2001-06

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  • Abstract

In this paper we modify type approximate trust region methods via two curvilinear paths for unconstrained optimization. A mixed strategy using both trust region and line search techniques is adopted which switches to back tracking steps when a trial step produced by the trust region subproblem is unacceptable. We give a series of properties of both optimal path and modified gradient path. The global convergence and fast local convergence rate of the proposed algorithms are established under some reasonable conditions. A nonmonotonic criterion is used to speed up the convergence progress in some ill-conditioned cases.  

  • Keywords

Curvilinear paths, Trust region methods, Nonmonotonic technique, Unconstrained optimization.

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COPYRIGHT: © Global Science Press

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@Article{JCM-19-241, author = {Zhu , De-Tong}, title = {Curvilinear Paths and Trust Region Methods with Nonmonotonic Back Tracking Technique for Unconstrained Optimization}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {3}, pages = {241--258}, abstract = {

In this paper we modify type approximate trust region methods via two curvilinear paths for unconstrained optimization. A mixed strategy using both trust region and line search techniques is adopted which switches to back tracking steps when a trial step produced by the trust region subproblem is unacceptable. We give a series of properties of both optimal path and modified gradient path. The global convergence and fast local convergence rate of the proposed algorithms are established under some reasonable conditions. A nonmonotonic criterion is used to speed up the convergence progress in some ill-conditioned cases.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8977.html} }
TY - JOUR T1 - Curvilinear Paths and Trust Region Methods with Nonmonotonic Back Tracking Technique for Unconstrained Optimization AU - Zhu , De-Tong JO - Journal of Computational Mathematics VL - 3 SP - 241 EP - 258 PY - 2001 DA - 2001/06 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8977.html KW - Curvilinear paths, Trust region methods, Nonmonotonic technique, Unconstrained optimization. AB -

In this paper we modify type approximate trust region methods via two curvilinear paths for unconstrained optimization. A mixed strategy using both trust region and line search techniques is adopted which switches to back tracking steps when a trial step produced by the trust region subproblem is unacceptable. We give a series of properties of both optimal path and modified gradient path. The global convergence and fast local convergence rate of the proposed algorithms are established under some reasonable conditions. A nonmonotonic criterion is used to speed up the convergence progress in some ill-conditioned cases.  

Zhu , De-Tong. (2001). Curvilinear Paths and Trust Region Methods with Nonmonotonic Back Tracking Technique for Unconstrained Optimization. Journal of Computational Mathematics. 19 (3). 241-258. doi:
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