A BFGS trust-region method for nonlinear equations

In this paper, a new trust-region subproblem combining with the BFGS update is proposed for solving nonlinear equations, where the trust region radius is defined by a new way. The global convergence without the nondegeneracy assumption and the quadratic convergence are obtained under suitable condit...

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Veröffentlicht in:Computing Jg. 92; H. 4; S. 317 - 333
Hauptverfasser: Yuan, Gonglin, Wei, Zengxin, Lu, Xiwen
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Vienna Springer Vienna 01.08.2011
Springer
Springer Nature B.V
Schlagworte:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Artificial Intelligence
Computation
Computer Appl. in Administrative Data Processing
Computer Communication Networks
Computer Science
Computer science; control theory; systems
Convergence
Exact sciences and technology
Information Systems Applications (incl.Internet)
Mathematical models
Mathematics
Methods
Methods of scientific computing (including symbolic computation, algebraic computation)
Nonlinear equations
Norms
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Sciences and techniques of general use
Software Engineering
Studies
Theoretical computing
Global convergence
Nonlinear equations
90C26
65K05
BFGS update
Trust region method
Numerical method
Stochastic method
Algorithm
Convergence
Non linear equation
Numerical analysis
Scientific computation
ISSN:0010-485X, 1436-5057
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:In this paper, a new trust-region subproblem combining with the BFGS update is proposed for solving nonlinear equations, where the trust region radius is defined by a new way. The global convergence without the nondegeneracy assumption and the quadratic convergence are obtained under suitable conditions. Numerical results show that this method is more effective than the norm method.
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ISSN:0010-485X
1436-5057
DOI:10.1007/s00607-011-0146-z