Encyclopedia of Optimization

Editors: Christodoulos A. Floudas, Panos M. Pardalos

Broyden Family of Methods and the BFGS Update

BFM
  • Vassilios S. Vassiliadis
  • Raúl Conejeros
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-74759-0_61

Article Outline

Keywords

See also

References

Keywords

Unconstrained optimization BFGS update DFP update Broyden family of methods Rank-two updates Quasi-Newton methods 
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References

  1. 1.
    Broyden CG (1970) The convergence of a class of double rank minimization algorithms. Part I. J Inst Math Appl 6:76–90MathSciNetCrossRefMATHGoogle Scholar
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    Broyden CG (1970) The convergence of a class of double rank minimization algorithms. Part II. J Inst Math Appl 6:222–231MathSciNetCrossRefMATHGoogle Scholar
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    Davidon WC (1959) Variable metric method for minimization. Techn Report AEC Res Developm ANL-5590Google Scholar
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    Fletcher R (1970) A new approach to variable metric algorithms. Comput J 13:317–322CrossRefMATHGoogle Scholar
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    Fletcher R (1991) Practical methods of optimization, 2nd edn. Wiley, New YorkGoogle Scholar
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    Fletcher R, Powell MJD (1963) A rapidly convergent descent method for minimization. Comput J 6:163–168MathSciNetMATHGoogle Scholar
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    Goldfarb D (1970) A family of variable metric methods derived by variational means. Math Comput 24:23–26MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Luenberger DG (1984) Linear and nonlinear programming, 2nd edn. Addison-Wesley, Reading, MAMATHGoogle Scholar
  9. 9.
    Shanno DF (1970) Conditioning of quasi-Newton methods for function minimization. Math Comput 24:647–656MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Vassilios S. Vassiliadis
    • 1
  • Raúl Conejeros
    • 1
  1. 1.Chemical Engineering DepartmentUniversity CambridgeCambridgeUK