A New Nonmonotone Adaptive Retrospective Trust Region Method for Unconstrained Optimization Problems

In this paper, we propose a new nonmonotone adaptive retrospective Trust Region (TR) method for solving unconstrained optimization problems. Inspired by the retrospective ratio proposed in Bastin et al. (Math Program Ser A 123:395–418, 2010 ), a new nonmonotone TR ratio is introduced based on a conv...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2015-11, Vol.167 (2), p.676-692
Main Authors: Tarzanagh, D. Ataee, Peyghami, M. Reza, Bastin, F.
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control
Optimization
Computational efficiency
Computing time
Convergence
Engineering
Mathematical models
Mathematics
Mathematics and Statistics
Methods
Operations Research/Decision Theory
Optimization
Ratios
Studies
Theory of Computation
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Summary:In this paper, we propose a new nonmonotone adaptive retrospective Trust Region (TR) method for solving unconstrained optimization problems. Inspired by the retrospective ratio proposed in Bastin et al. (Math Program Ser A 123:395–418, 2010 ), a new nonmonotone TR ratio is introduced based on a convex combination of the nonmonotone classical and retrospective ratios. Due to the value of the new ratio, the TR radius is updated adaptively by a variant of the rule as proposed in Shi and Guo (J Comput Appl Math 213:509–520, 2008 ). Global convergence property of the new algorithm, as well as its superlinear convergence rate, is established under some standard assumptions. Numerical results on some test problems show the efficiency and effectiveness of the new method in practice, too.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-015-0790-0