Journal of Optimization Theory and Applications

, Volume 172, Issue 2, pp 578–593

# Local Stability and Local Convergence of the Basic Trust-Region Method

• Bui Ngoc Muoi
• Nguyen Dong Yen
Article

## 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.

## Keywords

Unconstrained smooth optimization problem Basic trust-region method Iterative sequence Stability Linear convergence

## Mathematics Subject Classification

90C30 90C26 49M37

## Notes

### 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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