BIT Numerical Mathematics

, Volume 21, Issue 3, pp 362–373 | Cite as

Globally convergent methods for semi-infinite programming

  • G. A. Watson
Part II. Numerical Mathematics

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.

Keywords

Computational Mathematic Programming Problem Penalty Function Convergence Property Convergence Result 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Beale, E. M.,Numerical methods, inNonlinear Programming, ed. J. Abadie, North Holland, Amsterdam (1967).Google Scholar
  2. 2.
    Clarke, F. H.,A new approach to Lagrange multipliers, Mathematics of Operations Research 1, 165–174 (1976).Google Scholar
  3. 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.Google Scholar
  4. 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).Google Scholar
  5. 5.
    Fletcher, R.,Practical Methods of Optimization, Vol. II. Constrained Optimization, Wiley, Chichester (1981).Google Scholar
  6. 6.
    Han, S. P.,Superlinearly convergent variable metric algorithms for general nonlinear programming problems, Math. Prog. 11, 263–282 (1976).Google Scholar
  7. 7.
    Han, S. P.,A globally convergent method for nonlinear programming, J. of Opt. Th. and Appl. 22, 297–309 (1977).Google Scholar
  8. 8.
    Hettich, R. ed.Semi-infinite Programming, Proceedings of a Workshop, Springer-Verlag, Berlin (1979).Google Scholar
  9. 9.
    Hettich, R. and W. van Honstede,On quadratically convergent methods for semi-infinite programming, in [8], 97–111, (1979).Google Scholar
  10. 10.
    van Honstede, W.,An approximation method for semi-infinite problems, in [8],, 126–136 (1979).Google Scholar
  11. 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. 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. 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).Google Scholar
  14. 14.
    Wilson, R. B.,A simplicial algorithm for concave programming, Ph.D. dissertation, Graduate School of Business Administration, Harvard University (1963).Google Scholar

Copyright information

© BIT Foundations 1981

Authors and Affiliations

  • G. A. Watson
    • 1
  1. 1.Department of MathematicsUniversity of DundeeScotland

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