Skip to main content

Newton-type algorithms with nonmonotone line search for large-scale unconstrained optimization

  • Continuous Estimation
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 113))

Abstract

In this paper we define globally convergent algorithms for the solution of large dimensional unconstrained minimization problems. The algorithms proposed employ a nonmonotone steplength selection rule along the search direction which is determined by means of a Truncated-Newton algorithm. Numerical results obtained for a set of test problems are reported.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R.S. Dembo, S.C. Eisenstat and T. Steihaug, Inexact Newton methods, SIAM J. Numer. Anal., 19 (1982), pp.400–408.

    Google Scholar 

  2. R.S. Dembo and T. Steihaug, Truncated-Newton algorithms for large-scale unconstrained optimization, Math. Prog., 26 (1983), pp.190–212.

    Google Scholar 

  3. L.C.W. Dixon and R.C. Price, Numerical experience with the Truncated-Newton method, Tech. Rep. No. 169, Numerical Optimization Centre, The Hatfield Polytechnic, Hatfield, UK, 1986.

    Google Scholar 

  4. L. Grippo, F. Lampariello and S. Lucidi, A Truncated-Newton method with nonmonotone line search for unconstrained optimization, J. Optim. Theory Appl., (to appear).

    Google Scholar 

  5. L. Grippo, F. Lampariello and S. Lucidi, A nonmonotone line search technique for Newton's method, SIAM J. Numer. Anal., 23 (1986), pp.707–716.

    Google Scholar 

  6. D.P. Bertsekas, Constrained optimization and Lagrange multiplier methods, Academic Press, New York, 1982.

    Google Scholar 

  7. M.R. Hestenes, Conjugate direction methods in optimization, Springer-Verlag, New York, 1980.

    Google Scholar 

  8. N.K. Garg and R.A. Tapia, QDN: A variable storage algorithm for unconstrained optimization, Tech. Rep., Department of Mathematical Sciences, Rice University, Houston, TX, 1977.

    Google Scholar 

  9. J.P. Bulteau and J.P. Vial, A restricted trust region algorithm for unconstrained optimization, J. Optim. Theory Appl., 47 (1985), pp.413–435.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Masao Iri Keiji Yajima

Rights and permissions

Reprints and permissions

Copyright information

© 1988 International Federation for Information Processing

About this paper

Cite this paper

Grippo, L., Lampariello, F., Lucidi, S. (1988). Newton-type algorithms with nonmonotone line search for large-scale unconstrained optimization. In: Iri, M., Yajima, K. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042786

Download citation

  • DOI: https://doi.org/10.1007/BFb0042786

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19238-1

  • Online ISBN: 978-3-540-39164-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics