An improved nonmonotone adaptive trust region method

Yanqin Xue; Hongwei Liu; Zexian Liu

Applications of Mathematics (2019)

  • Volume: 64, Issue: 3, page 335-350
  • ISSN: 0862-7940

Abstract

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Trust region methods are a class of effective iterative schemes in numerical optimization. In this paper, a new improved nonmonotone adaptive trust region method for solving unconstrained optimization problems is proposed. We construct an approximate model where the approximation to Hessian matrix is updated by the scaled memoryless BFGS update formula, and incorporate a nonmonotone technique with the new proposed adaptive trust region radius. The new ratio to adjusting the next trust region radius is different from the ratio in the traditional trust region methods. Under some suitable and standard assumptions, it is shown that the proposed algorithm possesses global convergence and superlinear convergence. Numerical results demonstrate that the proposed method is very promising.

How to cite

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Xue, Yanqin, Liu, Hongwei, and Liu, Zexian. "An improved nonmonotone adaptive trust region method." Applications of Mathematics 64.3 (2019): 335-350. <http://eudml.org/doc/294424>.

@article{Xue2019,
abstract = {Trust region methods are a class of effective iterative schemes in numerical optimization. In this paper, a new improved nonmonotone adaptive trust region method for solving unconstrained optimization problems is proposed. We construct an approximate model where the approximation to Hessian matrix is updated by the scaled memoryless BFGS update formula, and incorporate a nonmonotone technique with the new proposed adaptive trust region radius. The new ratio to adjusting the next trust region radius is different from the ratio in the traditional trust region methods. Under some suitable and standard assumptions, it is shown that the proposed algorithm possesses global convergence and superlinear convergence. Numerical results demonstrate that the proposed method is very promising.},
author = {Xue, Yanqin, Liu, Hongwei, Liu, Zexian},
journal = {Applications of Mathematics},
keywords = {unconstrained optimization; trust region method; scaled memoryless BFGS update; nonmonotone technique; global convergence},
language = {eng},
number = {3},
pages = {335-350},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An improved nonmonotone adaptive trust region method},
url = {http://eudml.org/doc/294424},
volume = {64},
year = {2019},
}

TY - JOUR
AU - Xue, Yanqin
AU - Liu, Hongwei
AU - Liu, Zexian
TI - An improved nonmonotone adaptive trust region method
JO - Applications of Mathematics
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 3
SP - 335
EP - 350
AB - Trust region methods are a class of effective iterative schemes in numerical optimization. In this paper, a new improved nonmonotone adaptive trust region method for solving unconstrained optimization problems is proposed. We construct an approximate model where the approximation to Hessian matrix is updated by the scaled memoryless BFGS update formula, and incorporate a nonmonotone technique with the new proposed adaptive trust region radius. The new ratio to adjusting the next trust region radius is different from the ratio in the traditional trust region methods. Under some suitable and standard assumptions, it is shown that the proposed algorithm possesses global convergence and superlinear convergence. Numerical results demonstrate that the proposed method is very promising.
LA - eng
KW - unconstrained optimization; trust region method; scaled memoryless BFGS update; nonmonotone technique; global convergence
UR - http://eudml.org/doc/294424
ER -

References

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