Nonmonotone trust region algorithm for unconstrained optimization problems
type: Item
instance of: scholarly article
title: Nonmonotone trust region algorithm for unconstrained optimization problems
zbMATH Open document ID: 1210.65120
author: Qing-Jun Wu
published in: Applied Mathematics and Computation
publication date: 2011-01-14T00:00:00Z
review text: The usual trust region methods generate a sequence of iterates such that the objective function value sequence is monotonically decreasing; hence, they accept the trial step if the objective function has decreased sufficiently. It is proven that trust region method has strong convergence property and is efficient for optimization problem. However, a lot of numerical experiments indicate that enforcing monotonicity of the objective function value sequence may considerably slow the rate of convergence when the iteration is trapped near a narrow curved valley. Recent researches indicate that it might be advantageous to allow the algorithm to generate a nonmonotone objective function value sequence. In this paper, the authors present a new, nonmonotone trust region algorithm for unconstrained optimization problems. This method combines the nonmonotone technique proposed by \textit{H. Zhang} and \textit{W. W. Hanger} [SIAM J. Optim. 14, No.~4, 1043--1056 (2004; Zbl 1073.90024)] with the trust region method proposed by \textit{P. L. Toint} [Math. Program. 77, No.~1 (A), 69--94 (1997; Zbl 0891.90153)]. The method is also independent on the choice of parameter. Under suitable assumptions, global and superlinear convergence results are proved. The numerical results show that the presented method is efficient.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C51
zbMATH DE Number: 5836723
zbMATH Keywords: trust region method
zbMATH Keywords: unconstrained optimization
zbMATH Keywords: nonmonotone technique
zbMATH Keywords: global convergence
zbMATH Keywords: superlinear convergence
zbMATH Keywords: numerical results
reviewed by: Nada Djuranović-Miličić
describes a project that uses: minpack
MaRDI profile type: Publication
full work available at URL: j.amc.2010.09.044
OpenAlex ID: W1970529249
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DOI: 10.1016/J.AMC.2010.09.044
description: scientific article; zbMATH DE number 5836723