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Abstract

It is proved that the iterative sequence constructed by the Basic Trust-Region Algorithm (see Conn et al. in Trust-region methods, MPS-SIAM series on optimization, Philadelphia, 2000), which uses the Cauchy point method, is locally stable and linearly convergent in a neighborhood of a nonsingular local minimizer.

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Acknowledgements

Research of B.N. Muoi was supported by Hanoi Pedagogical University No. 2 (Vietnam) under Grant Number C.2016.12. Research of N.D. Yen was supported by the project VAST.HTQT.Pháp.03/16-17 between VAST and CNRS. We thank the anonymous referee for helpful comments and suggestions.

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Correspondence to Nguyen Dong Yen.

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Communicated by Suliman Saleh Al-Homidan.

Dedicated to Professor B.T. Polyak on the occasion of his 80th birthday.

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Muoi, B.N., Yen, N.D. Local Stability and Local Convergence of the Basic Trust-Region Method. J Optim Theory Appl 172, 578–593 (2017). https://doi.org/10.1007/s10957-016-1038-3

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  • DOI: https://doi.org/10.1007/s10957-016-1038-3

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