Local Stability and Local Convergence of the Basic Trust-Region Method
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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.
KeywordsUnconstrained smooth optimization problem Basic trust-region method Iterative sequence Stability Linear convergence
Mathematics Subject Classification90C30 90C26 49M37
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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