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Open AccessArticle

A New Filter Nonmonotone Adaptive Trust Region Method for Unconstrained Optimization

by Xinyi Wang 1, Xianfeng Ding 1,2,* and Quan Qu 1
1
School of Science, Southwest Petroleum University, Chengdu 610500, China
2
School of Artificial Intelligence, Southwest Petroleum University, Chengdu 610500, China
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(2), 208; https://doi.org/10.3390/sym12020208
Received: 17 December 2019 / Revised: 20 January 2020 / Accepted: 21 January 2020 / Published: 2 February 2020
(This article belongs to the Special Issue Advance in Nonlinear Analysis and Optimization)
In this paper, a new filter nonmonotone adaptive trust region with fixed step length for unconstrained optimization is proposed. The trust region radius adopts a new adaptive strategy to overcome additional computational costs at each iteration. A new nonmonotone trust region ratio is introduced. When a trial step is not successful, a multidimensional filter is employed to increase the possibility of the trial step being accepted. If the trial step is still not accepted by the filter set, it is possible to find a new iteration point along the trial step and the step length is computed by a fixed formula. The positive definite symmetric matrix of the approximate Hessian matrix is updated using the MBFGS method. The global convergence and superlinear convergence of the proposed algorithm is proven by some classical assumptions. The efficiency of the algorithm is tested by numerical results.
Keywords: unconstrained optimization; adaptive trust region; nonmonotone; filter; convergence unconstrained optimization; adaptive trust region; nonmonotone; filter; convergence
MDPI and ACS Style

Wang, X.; Ding, X.; Qu, Q. A New Filter Nonmonotone Adaptive Trust Region Method for Unconstrained Optimization. Symmetry 2020, 12, 208.

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