Skip to main content
SpringerLink
Log in

An exact penalty function method with global convergence properties for nonlinear programming problems

  • Published:
Mathematical Programming Submit manuscript

Abstract

In this paper a new continuously differentiable exact penalty function is introduced for the solution of nonlinear programming problems with compact feasible set. A distinguishing feature of the penalty function is that it is defined on a suitable bounded open set containing the feasible region and that it goes to infinity on the boundary of this set. This allows the construction of an implementable unconstrained minimization algorithm, whose global convergence towards Kuhn-Tucker points of the constrained problem can be 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. D.P. Bertsekas,Constrained Optimization and Lagrange Multiplier Methods (Academic Press, New York, 1982).

    MATH  Google Scholar 

  2. A.R. Conn, “Penalty function methods”, in: M.J.D. Powell, ed.,Nonlinear Optimization 1981 (Academic Press, New York, 1982) pp. 235–242.

    Google Scholar 

  3. G. Di Pillo and L. Grippo, “A class of continuously differentiable exact penalty function algorithms for nonlinear programming problems,” in: P. Toft-Christensen, ed.,System Modelling and Optimization (Springer-Verlag, Berlin, 1984) pp. 246–256.

    Chapter  Google Scholar 

  4. G. Di Pillo and L. Grippo, “An exact penalty method with global convergence properties for nonlinear programming problems”, Technical Report R.99, IASI-CNR (Roma, October 1984).

  5. G. Di Pillo and L. Grippo, “A continuously differentiable exact penalty function for nonlinear programming problems with inequality constraints”,SIAM Journal on Control and Optimization 23 (1985) 72–84.

    Article  MATH  MathSciNet  Google Scholar 

  6. G. Di Pillo, L. Grippo and S. Lucidi, “Globally convergent exact penalty algorithms for constrained optimization”, Contributed paper, 12th IFIP Conference on System Modelling and Optimization, Budapest, September 1985.

  7. J.P. Evans, F.J. Gould and J.W. Tolle, “Exact penalty functions in nonlinear programming”,Mathematical Programming 4 (1973) 72–97.

    Article  MATH  MathSciNet  Google Scholar 

  8. A.V. Fiacco and G.P. McCormick,Nonlinear Programming: Sequential Unconstrained Minimization Techniques (Wiley, New York, 1968).

    MATH  Google Scholar 

  9. R. Fletcher, “A class of methods for nonlinear programming with termination and convergence properties”, in: J. Abadie, ed.,Integer and Nonlinear Programming (North-Holland, Amsterdam, 1970) pp. 157–173.

    Google Scholar 

  10. R. Fletcher, “Penalty functions”, in: A. Bachem, M. Grötschel and B. Korte, eds.,Mathematical Programming. The State of the Art (Springer-Verlag, Berlin, 1983) pp. 87–114.

    Google Scholar 

  11. T. Glad and E. Polak, “A multiplier method with automatic limitation of penalty growth”,Mathematical Programming 17 (1979) 140–155.

    Article  MATH  MathSciNet  Google Scholar 

  12. S.P. Han and O.L. Mangasarian, “Exact penalty functions in nonlinear programming”,Mathematical Programming 17 (1979) 251–269.

    Article  MATH  MathSciNet  Google Scholar 

  13. O. L. Mangasarian,Nonlinear Programming (Prentice-Hall, Englewood Cliffs, NJ, 1969).

    MATH  Google Scholar 

  14. D.Q. Mayne and N. Maratos, “A first order, exact penalty function algorithm for equality constrained optimization problems”,Mathematical Programming 16 (1979) 303–324.

    Article  MATH  MathSciNet  Google Scholar 

  15. D.Q. Mayne and E. Polak, “A superlinearly convergent algorithm for constrained optimization problems”,Mathematical Programming Study 16 (1982) 45–61.

    MATH  MathSciNet  Google Scholar 

  16. N. Mukai and E. Polak, “A quadratically convergent primal-dual algorithm with global convergence properties for solving optimization problems with equality constraints”,Mathematical Programming 9 (1975) 336–349.

    Article  MATH  MathSciNet  Google Scholar 

  17. T. Pietrzykowski, “An exact potential method for constrained maxima”,SIAM Journal on Numerical Analysis 6 (1969) 294–304.

    MathSciNet  Google Scholar 

  18. E. Polak, “On the global stabilization of locally convergent algorithms”,Automatica 12 (1976) 337–342.

    Article  MATH  MathSciNet  Google Scholar 

  19. J.E. Spingarn and R.T. Rockafellar, “The generic nature of optimality conditions in nonlinear programming”,Mathematics of Operations Research 4 (1979) 425–430.

    MATH  MathSciNet  Google Scholar 

  20. W.I. Zangwill, “Nonlinear programming via penalty functions”,Management Science 13 (1967) 344–358.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, Università di Roma ‘La Sapienza’, Via Eudossiana 18, 00184, Roma, Italy

    G. Di Pillo

  2. Istituto di Analisi dei Sistemi ed Informatica, Consiglio Nazionale delle Ricerche, Viale Manzoni 30, 00185, Roma, Italy

    L. Grippo

Authors
  1. G. Di Pillo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Grippo
    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

Di Pillo, G., Grippo, L. An exact penalty function method with global convergence properties for nonlinear programming problems. Mathematical Programming 36, 1–18 (1986). https://doi.org/10.1007/BF02591986

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02591986

Key words

Search

Navigation