An adaptive trust region method and its convergence

Xiangsun Zhang; Juliang Zhang; Lizhi Liao

An adaptive trust region method and its convergence

Xiangsun Zhang, Juliang Zhang^*, Lizhi Liao

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

81 Citations (Scopus)

Abstract

In this paper, a new trust region subproblem is proposed. The trust radius in the new subproblem adjusts itself adaptively. As a result, an adaptive trust region method is constructed based on the new trust region subproblem. The local and global convergence results of the adaptive trust region method are proved. Numerical results indicate that the new method is very efficient.

Original language	English
Pages (from-to)	620-631
Number of pages	12
Journal	Science China Mathematics
Volume	45
Issue number	5
Publication status	Published - May 2002

Scopus Subject Areas

Mathematics(all)

User-Defined Keywords

Global convergence
Super-linear convergence
Trust region method
Unconstrained optimization

Cite this

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title = "An adaptive trust region method and its convergence",

abstract = "In this paper, a new trust region subproblem is proposed. The trust radius in the new subproblem adjusts itself adaptively. As a result, an adaptive trust region method is constructed based on the new trust region subproblem. The local and global convergence results of the adaptive trust region method are proved. Numerical results indicate that the new method is very efficient.",

keywords = "Global convergence, Super-linear convergence, Trust region method, Unconstrained optimization",

author = "Xiangsun Zhang and Juliang Zhang and Lizhi Liao",

note = "Funding Information: Acknowledgements The authors would like to thank Prof Y.-X. Yuan for providing the source programs for ref. [16]. Zhang Xiangsun was supported by the National Natural Science Foundation of China (Grant No. 39830070) and Hong Kong Baptist University; Zhang Juliang was supported by the National Natural Science Foundation of China (Grant No. 10171055); Liao Lizhi was supported by Hong Kong Baptist University.",

year = "2002",

month = may,

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TY - JOUR

T1 - An adaptive trust region method and its convergence

AU - Zhang, Xiangsun

AU - Zhang, Juliang

AU - Liao, Lizhi

N1 - Funding Information: Acknowledgements The authors would like to thank Prof Y.-X. Yuan for providing the source programs for ref. [16]. Zhang Xiangsun was supported by the National Natural Science Foundation of China (Grant No. 39830070) and Hong Kong Baptist University; Zhang Juliang was supported by the National Natural Science Foundation of China (Grant No. 10171055); Liao Lizhi was supported by Hong Kong Baptist University.

PY - 2002/5

Y1 - 2002/5

N2 - In this paper, a new trust region subproblem is proposed. The trust radius in the new subproblem adjusts itself adaptively. As a result, an adaptive trust region method is constructed based on the new trust region subproblem. The local and global convergence results of the adaptive trust region method are proved. Numerical results indicate that the new method is very efficient.

AB - In this paper, a new trust region subproblem is proposed. The trust radius in the new subproblem adjusts itself adaptively. As a result, an adaptive trust region method is constructed based on the new trust region subproblem. The local and global convergence results of the adaptive trust region method are proved. Numerical results indicate that the new method is very efficient.

KW - Global convergence

KW - Super-linear convergence

KW - Trust region method

KW - Unconstrained optimization

UR - https://link.springer.com/article/10.1360/02ys9067

UR - http://www.scopus.com/inward/record.url?scp=0038821465&partnerID=8YFLogxK

M3 - Journal article

AN - SCOPUS:0038821465

SN - 1674-7283

VL - 45

SP - 620

EP - 631

JO - Science China Mathematics

JF - Science China Mathematics

IS - 5

ER -

An adaptive trust region method and its convergence

Abstract

Scopus Subject Areas

User-Defined Keywords

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