Skip to main content
SpringerLink
Log in

An exact penalty approach to constrained minimization problems on metric spaces

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

In this paper we use the penalty approach in order to study a class of constrained minimization problems on complete metric spaces. A penalty function is said to have the generalized exact penalty property if there is a penalty coefficient for which approximate solutions of the unconstrained penalized problem are close enough to approximate solutions of the corresponding constrained problem. For our class of problems we establish the generalized exact penalty property and obtain an estimation of the exact penalty.

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. Boukari D., Fiacco A.V.: Survey of penalty, exact-penalty and multiplier methods from 1968 to 1993. Optimization 32, 301–334 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  2. Clarke F.H.: Optimization and nonsmooth analysis. Wiley, New York (1983)

    MATH  Google Scholar 

  3. Demyanov V.F.: Extremum conditions and variational problems. St. Peterb. Gos. Univ., St. Petersburg (2000)

    Google Scholar 

  4. Demyanov V.F.: Exact penalty functions and problems of the calculus of variations. Avtomat. i Telemekh. 2, 136–147 (2004)

    MathSciNet  Google Scholar 

  5. Demyanov V.F., Di Pillo G., Facchinei F.: Exact penalization via Dini and Hadamard conditional derivatives. Optim. Methods Softw. 9, 19–36 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Di Pillo G., Grippo L.: Exact penalty functions in constrained optimization. SIAM J. Control Optim. 27, 1333–1360 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  7. Ekeland I.: On the variational principle. J. Math. Anal. Appl. 47, 324–353 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  8. Eremin I.I.: The penalty method in convex programming. Sov. Math. Dokl. 8, 459–462 (1966)

    Google Scholar 

  9. Mordukhovich B.S.: Variational analysis and generalized differentiation, II: applications. Springer, Berlin (2006)

    Google Scholar 

  10. Zangwill W.I.: Nonlinear programming via penalty functions. Manag. Sci. 13, 344–358 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  11. Zaslavski A.J.: A sufficient condition for exact penalty in constrained optimization. SIAM J. Optim. 16, 250–262 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Zaslavski A.J.: Existence of approximate exact penalty in constrained optimization. Math. Oper. Res. 32, 484–495 (2007)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, The Technion-Israel Institute of Technology, 32000, Haifa, Israel

    Alexander J. Zaslavski

Authors
  1. Alexander J. Zaslavski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexander J. Zaslavski.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zaslavski, A.J. An exact penalty approach to constrained minimization problems on metric spaces. Optim Lett 7, 1009–1016 (2013). https://doi.org/10.1007/s11590-012-0500-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-012-0500-x

Keywords

Mathematics Subject Classification

Search

Navigation