Journal of Optimization Theory and Applications

, Volume 56, Issue 2, pp 245–255

Numerical experience with the truncated Newton method for unconstrained optimization

  • L. C. W. Dixon
  • R. C. Price
Contributed Papers

Abstract

The truncated Newton algorithm was devised by Dembo and Steihaug (Ref. 1) for solving large sparse unconstrained optimization problems. When far from a minimum, an accurate solution to the Newton equations may not be justified. Dembo's method solves these equations by the conjugate direction method, but truncates the iteration when a required degree of accuracy has been obtained. We present favorable numerical results obtained with the algorithm and compare them with existing codes for large-scale optimization.

Key Words

Unconstrained optimization truncated Newton method sparsity trust region 

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References

  1. 1.
    Dembo, R., andSteihaug, T.,Truncated Newton Algorithms for Large-Scale Optimization, Mathematical Programming, Vol. 26, pp. 190–212, 1983.Google Scholar
  2. 2.
    Hestenes, M. R., andStiefel, E.,Methods of Conjugate Gradients for Solving Linear Systems, Journal of Research of the National Bureau of Standards, Vol. 49, pp. 409–436, 1952.Google Scholar
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    Steihaug, T.,The Conjugate Gradient Method and Trust Regions in Large-Scale Optimization, SIAM Journal on Numerical Analysis, Vol. 20, pp. 626–637, 1983.Google Scholar
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    Dembo, R., Eisenstat, S. C., andSteihaug, T.,Inexact Newton Methods, SIAM Journal on Numerical Analysis, Vol. 19, pp. 400–408, 1982.Google Scholar
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    Dixon, L. C. W., Ducksbury, P. G., andSingh, P.,A New Three-Term Conjugate Gradient Method, Journal of Optimization Theory and Applications, Vol. 47, pp. 285–300, 1985.Google Scholar
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    Anonymous, N. N.,Optima Manual, Numerical Optimization Centre, Hatfield Polytechnic, 1984.Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • L. C. W. Dixon
    • 1
  • R. C. Price
    • 1
  1. 1.Numerical Optimization CentreHatfield PolytechnicHatfieldEngland

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