Skip to main content

On the methods of nonsmooth optimization

  • Nonlinear Optimization
  • Conference paper
  • First Online:
Book cover System Modelling and Optimization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 143))

Abstract

In this paper we shall give a short derivation of the most promising methods in nonsmooth optimization, namely bundle methods. We introduce the basic bundle idea due to Lemarechal and several modifications by Kiwiel, Schramm and Zowe. To the end we shall give some numerical results comparing the efficience of these methods. As test problems we have used well-known test problems from litterature and in addition we shall give some contributions to nonsmooth optimal control problems.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Gaudioso M. and Monaco M. F., Some Techniques for Finding the Search Direction in Nonsmooth Minimization Problems, Dip. Sist. Univ. Calabria, Rep. 75 (1988).

    Google Scholar 

  2. Kiwiel K. C., “Methods of Descent for Nondifferentiable Optimization,” Lecture Notes in Mathematics 1133, Springer-Verlag, Berlin, 1985.

    Google Scholar 

  3. Kiwiel K. C., Proximity Control in Bundle Methods for Convex Nondifferentiable Optimization, Preprint, System Research Institute, Polish Academy of Sciences, Warsaw (1987).

    Google Scholar 

  4. Lemaréchal C., Nondifferentiable Optimization, Subgradient and ɛ-subgradient Methods, Optimization and Operations Research, Lecture Notes in Economics and Mathematical Systems 117 (1976), 191–199.

    Google Scholar 

  5. Lemaréchal C., Nondifferentiable Optimization, in “Handbooks in OR & MS,” (Eds. Nemhauser G. L. et al.), North Holland, 1989.

    Google Scholar 

  6. Miflin R., A modification and an Extension of Lemaréchal's Algorithm for Nonsmooth Optimization, Mathematical Programming Study 17 (1982), 77–90.

    Google Scholar 

  7. Mäkelä M. M., Subdifferential Analysis for Nonsmooth Optimization, Reports on Applied Mathematics and Computing, University of Jyväskylä, Department of Mathematics 3 (1988).

    Google Scholar 

  8. Mäkelä M. M., Methods and Algorithms for Nonsmooth Optimization, Reports on Applied Mathematics and Computing, University of Jyväskylä, Department of Mathematics 2 (1989).

    Google Scholar 

  9. Schramm H., “Eine Kombination von Bundle-und Trust-Region-Verfahren zur Lösung nichtdifferenzierbarer Optimierungsprobleme,” Bayreuther Mathematische Scriften, Bayreuth, 1989.

    Google Scholar 

  10. Shor N. Z., “Minimization Methods for Non-differentiable Functions,” Springer-Verlag, Berlin, 1985.

    Google Scholar 

  11. Zowe J., The BT-algorithm for Minimizing a Nonsmooth Functional Subject to Linear Constraints, Working paper in Department of Economics, University of Bergen, Norway 1088 (1988).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

H. -J. Sebastian K. Tammer

Rights and permissions

Reprints and permissions

Copyright information

© 1990 International Federation for Information Processing

About this paper

Cite this paper

Mäkelä, M.M. (1990). On the methods of nonsmooth optimization. In: Sebastian, H.J., Tammer, K. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 143. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0008368

Download citation

  • DOI: https://doi.org/10.1007/BFb0008368

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52659-9

  • Online ISBN: 978-3-540-47095-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics