A new simple model trust-region method with generalized Barzilai-Borwein parameter for large-scale optimization

In this paper, a new trust region method with simple model for solving large-scale unconstrained nonlinear optimization is proposed. By employing the generalized weak quasi-Newton equations, we derive several schemes to construct variants of scalar matrices as the Hessian approximation used in the t...

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Bibliographic Details
Published in:Science China. Mathematics 2016-11, Vol.59 (11), p.2265-2280
Main Authors: Zhou, QunYan, Sun, WenYu, Zhang, HongChao
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Approximation
Convergence
Efficiency
equation
trust
Hessian matrices
Libraries
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
method
global
method
weak
Optimization
optimization
Barzilai-Borwein
quasi-Newton
region
Scalars
Scale (ratio)
unconstrained
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Summary:In this paper, a new trust region method with simple model for solving large-scale unconstrained nonlinear optimization is proposed. By employing the generalized weak quasi-Newton equations, we derive several schemes to construct variants of scalar matrices as the Hessian approximation used in the trust region subproblem. Under some reasonable conditions, global convergence of the proposed algorithm is established in the trust region framework. The numerical experiments on solving the test problems with dimensions from 50 to 20,000 in the CUTEr library are reported to show efficiency of the algorithm.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-015-0734-2