Mathematical Programming

, Volume 26, Issue 2, pp 144–152 | Cite as

Revisions of constraint approximations in the successive QP method for nonlinear programming problems

  • Kaoru Tone
Article
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Revised:

Abstract

In the last few years the successive quadratic programming methods proposed by Han and Powell have been widely recognized as excellent means for solving nonlinea programming problems.

However, there remain some questions about their linear approximations to the constraints from both theoretical and empirical points of view.

In this paper, we propose two revisions of the linear approximation to the constraints and show that the directions generated by the revisions are also descent directions of exact penalty functions of nonlinear programming problems. The new technique can cope better with bad starting points than the usual one.

Key words

Nonlinear Programming Successive Quadratic Programming Method Linear Approximations Start Procedure Exact Penalty Function 
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References

  1. [1]
    M.C. Biggs, “Recursive quadratic programming methods for nonlinear constraints”, in: M.J.D. Powell, ed.,Nonlinear optimization 1981 (Academic Press, New York, 1982) pp. 213–221.Google Scholar
  2. [2]
    R.M. Chamberlain, C. Lemarechal, H.C. Pedersen and M.J.D. Powell, “The watchdog technique for forcing convergence in algorithms for constrained optimization”, DAMTP 80/NA9. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, (Cambridge 1980).Google Scholar
  3. [3]
    V.F. Dem'yanov and V.N. Malozemov,Introduction to minimax (John Wiley and Sons, New York, 1974).Google Scholar
  4. [4]
    S.P. Han, “A globally convergent method for nonlinear programming”,Journal of Optimization Theory and Applications 22 (1977) 297–309.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    M.J.D. Powell, “A fast algorithm for nonlinearly constrained optimization calculus”,Proceedings of the 1977 Dundee Biennial Conference on Numerical Analysis (Springer-Verlag, Berlin, 1978).Google Scholar

Copyright information

© North-Holland Publishing Company 1983

Authors and Affiliations

  • Kaoru Tone
    • 1
  1. 1.Graduate School for Policy ScienceSaitama UniversitySaitamaJapan

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