Skip to main content
SpringerLink
Log in

Globally convergent methods for semi-infinite programming

  • Part II. Numerical Mathematics
  • Published:
BIT Numerical Mathematics Aims and scope Submit manuscript

Abstract

Recently developed methods for nonlinear semi-infinite programming problems have only local convergence properties. In this paper, we show how the convergence can be globalized by the use of an exact penalty function. Both convergence and rate of convergence results are established.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Beale, E. M.,Numerical methods, inNonlinear Programming, ed. J. Abadie, North Holland, Amsterdam (1967).

    Google Scholar 

  2. Clarke, F. H.,A new approach to Lagrange multipliers, Mathematics of Operations Research 1, 165–174 (1976).

    Google Scholar 

  3. Fletcher, R.,A model algorithm for composite NDO problems, Workshop on Numerical Techniques in System Engineering, University of Kentucky, 1980, Proceedings to appear in Mathematical Programming Studies.

  4. Fletcher, R.,Numerical experiments with an exact L 1 penalty function method, Nonlinear Programming 4, Proceedings of Madison Conference, 1980, eds. O. L. Mangasarian, R. R. Meyer and S. M. Robinson (to appear).

  5. Fletcher, R.,Practical Methods of Optimization, Vol. II. Constrained Optimization, Wiley, Chichester (1981).

    Google Scholar 

  6. Han, S. P.,Superlinearly convergent variable metric algorithms for general nonlinear programming problems, Math. Prog. 11, 263–282 (1976).

    Google Scholar 

  7. Han, S. P.,A globally convergent method for nonlinear programming, J. of Opt. Th. and Appl. 22, 297–309 (1977).

    Google Scholar 

  8. Hettich, R. ed.Semi-infinite Programming, Proceedings of a Workshop, Springer-Verlag, Berlin (1979).

    Google Scholar 

  9. Hettich, R. and W. van Honstede,On quadratically convergent methods for semi-infinite programming, in [8], 97–111, (1979).

    Google Scholar 

  10. van Honstede, W.,An approximation method for semi-infinite problems, in [8],, 126–136 (1979).

    Google Scholar 

  11. Mayne, D. Q.,On the use of exact penalty functions to determine the step length in optimization algorithms, inNumerical Analysis, Dundee 1979, ed. G. A. Watson, Springer-Verlag, Berlin (1980).

    Google Scholar 

  12. Powell, M. J. D.,A fast algorithm for nonlinearly constrained optimization calculations, inNumerical Analysis, Dundee 1977, ed. G. A. Watson, Springer-Verlag, Berlin (1978).

    Google Scholar 

  13. Watson, G. A.,An algorithm for a class of nonlinearly constrained nondifferentiable optimization problems, Oberwolfach Conference on Finite Nonlinear Optimization 1980, ISNM 55, Birkhäuser Verlag (1980).

  14. Wilson, R. B.,A simplicial algorithm for concave programming, Ph.D. dissertation, Graduate School of Business Administration, Harvard University (1963).

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Dundee, Scotland

    G. A. Watson

Authors
  1. G. A. Watson
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Watson, G.A. Globally convergent methods for semi-infinite programming. BIT 21, 362–373 (1981). https://doi.org/10.1007/BF01941472

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01941472

Keywords

Search

Navigation