Skip to main content
SpringerLink
Log in

Exact penalty—Functions in infinite optimization

  • Conference paper
  • First Online:
Optimization and Optimal Control

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 477))

Abstract

For a class of penalty functions including those considered by Zangwill (7), Pietrzykowski (8) and Evans, Gould and Tolle (2) we show the essentialnecessary and sufficient properties for local exactness in an infinite dimensional optimization problem.

In particular we show that the local exactness property will follow by an inverse function theorem generalizing thus the results of Evans, Gould and Tolle. Next we generalize the results of Howe (5) and show in addition that the Kuhn-Tucker necessary conditions for a solution of the programming problem must be necessarily satisfied in order to have local exactness of our penalty function.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Czap H. Exact Penalty-Functions and Duality. Discussion paper Nr. 7402; Lehrstuhl für math. Verfahrensforschung (OR) und DV, Universität Göttingen.

    Google Scholar 

  2. evans J.P., Gould F.J., Tolle J.W. Exact Penalty Functions in Nonlinear Programming. Math. Progr. 4 (1973), 72–97.

    Article  MathSciNet  MATH  Google Scholar 

  3. Smirnov W.I. Lehrgang der Höheren Mathematik Teil V, Deutscher Verlag der Wissenschaften, Berlin 1967 (2. Auf1.).

    MATH  Google Scholar 

  4. Varaiya P.P. Nonlinear programming and optimal control. ERL Tech. Memo M—129, Univ. of California, Berkley 1965.

    Google Scholar 

  5. Howe S. New Conditions for Exactness of a simple Penalty Function. Siam J. Control 11 (1973) 378–381.

    Article  MathSciNet  MATH  Google Scholar 

  6. Ljusternik L.A., Sobolev W.I. Elemente der Funktionalanalysis, Akademie Verlag, Berlin, 1955.

    MATH  Google Scholar 

  7. Zangwill W.I. Nonlinear Programming via Penalty-functions. Management Science Vol. 13 (1967) 448–460.

    Google Scholar 

  8. Pietrzykowski T. An exact potential method for constrained maxima. Siam J. Num. Anal. 6 (1969) 299–304. Erratum: Vol. 8 (1971) p. 481.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lehrstuhl für mathematische Verfahrensforschung und Datenverarbeitung Universität Göttingen, Göttingen, Deutschland

    Hans Czap

Authors
  1. Hans Czap
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Technischen Universität München, 8 München, Postfach 202420, BRD

    Roland Bulirsch

  2. Fakultät für Mathematik und Informatik, Universität Mannheim, 68 Mannheim, Schloß, BRD

    Werner Oettli

  3. Institut für Angewandte Mathematik und Statistik der Universität Würzburg, 87 Würzburg, Am Hubland, BRD

    Josef Stoer

Rights and permissions

Reprints and permissions

Copyright information

© 1975 Springer-Verlag Berlin · Heidelberg

About this paper

Cite this paper

Czap, H. (1975). Exact penalty—Functions in infinite optimization. In: Bulirsch, R., Oettli, W., Stoer, J. (eds) Optimization and Optimal Control. Lecture Notes in Mathematics, vol 477. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079165

Download citation

  • DOI: https://doi.org/10.1007/BFb0079165

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07393-2

  • Online ISBN: 978-3-540-37591-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation