A new nonmonotone adaptive trust region method based on simple quadratic models

Based on simple quadratic models of the trust region subproblem, we combine the trust region method with the nonmonotone and adaptive techniques to propose a new nonmonotone adaptive trust region algorithm for unconstrained optimization. Unlike traditional trust region method, our trust region subpr...

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Bibliographic Details
Published in:Journal of applied mathematics & computing 2012-10, Vol.40 (1-2), p.111-123
Main Authors: Zhou, Qunyan, Zhang, Chun
Format: Article
Language:English
Subjects:
Adaptive algorithms
Algorithms
Applied mathematics
Approximation
Computation
Computational Mathematics and Numerical Analysis
Convergence
Mathematical analysis
Mathematical and Computational Engineering
Mathematical models
Mathematics
Mathematics and Statistics
Mathematics of Computing
Methods
Optimization
Original Research
Quadratic programming
Studies
Theory of Computation
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Summary:Based on simple quadratic models of the trust region subproblem, we combine the trust region method with the nonmonotone and adaptive techniques to propose a new nonmonotone adaptive trust region algorithm for unconstrained optimization. Unlike traditional trust region method, our trust region subproblem is very simple by using a new scale approximation of the minimizing function’s Hessian. The new method needs less memory capacitance and computational complexity. The convergence results of the method are proved under certain conditions. Numerical results show that the new method is effective and attractive for large scale unconstrained problems.
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-012-0572-x