Advertisement

Zeitschrift für Operations Research

, Volume 41, Issue 1, pp 25–55 | Cite as

A two parameter mixed interior-exterior penalty algorithm

  • Abdelhamid Benchakroun
  • Jean-Pierre Dussault
  • Abdelatif Mansouri
Articles

Abstract

In this paper, we analyze the mixed penalty methods introduced in the classic book of Fiacco and McCormick usingtwo distinct penalty parametersr, t. The two penalty coefficients induce a two-parameter differentiable trajectory. We analyze the numerical behaviour of an extrapolation strategy that follows the path of the two-parameter trajectory. We show also how to remove the ill-conditioning by suitable transformations of the equations. In the resulting theory, we show that function values as well as distances to the optimum are both governed by the same behaviour as interior methods (two-step superlinearly convergent, with limiting exponent 4/3).

Keywords

Penalty Method Classic Book Suitable Transformation Penalty Coefficient Numerical Behaviour 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Broyden CG, Attia NF (1988) Penalty functions, Newton's method, and quadratic programming. Journal of Optimization Theory and Applications 58/3Google Scholar
  2. 2.
    Courant R (1943) Variationnal methods for the solution of problems of equilibrium and vibrations. Bull Ameri Math soci 49Google Scholar
  3. 3.
    Dussault JP Numerical stability and efficiency of penalty algorithms. To appear S.I.A.M. Num AnalGoogle Scholar
  4. 4.
    Fiacco AV, et McCormick GP (1968) Nonlinear programming: Sequential unconstrained minimization techniques, Wiley, New-YorkGoogle Scholar
  5. 5.
    Frisch KR (1955) The logarithmic potential method of convex programming. Memorandum, University Institute of Economics, OsloGoogle Scholar
  6. 6.
    Gould NIM (1986) On the accurate determination of search directions for simple differentiable penalty functions. IMA J Numer Anal 6:357–372Google Scholar
  7. 7.
    Gould NIM (1989) On the convergence of a sequential penalty function method for constrained minimization. SIAM Numer Anal 26:107–128Google Scholar
  8. 8.
    McCormick GP (1989) The projective SUMT method for convex programming. M.O.R. 14: 203–223Google Scholar
  9. 9.
    Murray W (1969) Constrained optimization, University of London, PhD thesisGoogle Scholar
  10. 10.
    Wright MH (1992) Interior methods for latge-scale nonlinear optimization problems, presented at the fourth SIAM conference on Optimization, ChicagoGoogle Scholar

Copyright information

© Physica-Verlag 1995

Authors and Affiliations

  • Abdelhamid Benchakroun
    • 1
  • Jean-Pierre Dussault
    • 1
  • Abdelatif Mansouri
    • 1
  1. 1.Faculté des sciencesUniversité de SherbrookeSherbrookeCanada

Personalised recommendations