Skip to main content
SpringerLink
Log in

A multivalued approach to the Farkas lemma

  • Chapter
  • First Online:
Point-to-Set Maps and Mathematical Programming

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 10))

Abstract

The Farkas lemma is examined in the context of point-to-set mappings. Some general non-linear inclusions are studied and the standard linear results are rederived in a strengthened and simplified form.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. Berge, Topological spaces (Oliver and Boyd, London, 1963).

    MATH  Google Scholar 

  2. J.M. Borwein, “Multivalued convexity and optimization: a unified approach to equality and inequality constraints”, Mathematical Programming 13 (1977) 163–180.

    Article  Google Scholar 

  3. B.D. Craven, “Nonlinear programming in locally convex spaces”, Journal of Optimization Theory and Applications 10 (1972) 197–210.

    Article  MATH  MathSciNet  Google Scholar 

  4. T.M. Flett, “On differentiation in normed spaces”, Journal of the London Mathematical Society 42 (1967) 523–533.

    Article  MathSciNet  Google Scholar 

  5. D.H. Fremlin, Topological Riesz spaces and measure theory (Cambridge University Press, Cambridge, 1974).

    MATH  Google Scholar 

  6. K. Kuratowski, Topology, Volume 1 (revised) (Academic Press, New York, 1966).

    Google Scholar 

  7. R. Lehmann and W. Oettli, “The theorem of the alternative, the key theorem and the vector maximization problem, Mathematical Programming 8 (1975) 332–344.

    Article  MathSciNet  Google Scholar 

  8. O.L. Mangasarian, Nonlinear programming (McGraw-Hill, New York, 1969).

    MATH  Google Scholar 

  9. V.J. Manusco, “An Ascoli theorem for multivalued functions”, Journal of the Australian Mathematical Society 12 (1971) 466–477.

    Article  Google Scholar 

  10. A.L. Peressini, Ordered topological vector spaces (Harper and Row, New York, 1967).

    MATH  Google Scholar 

  11. K. Ritter, “Optimization in linear spaces, I”, Mathematische Annalen 182 (1969) 189–206.

    Article  MATH  MathSciNet  Google Scholar 

  12. K. Ritter, “Optimization in linear spaces, II”, Mathematische Annalen 183 (1969) 169–180.

    Article  MATH  MathSciNet  Google Scholar 

  13. K. Ritter, “Optimization in linear spaces, III”, Mathematische, Annalen 184 (1970) 133–154.

    Article  MATH  MathSciNet  Google Scholar 

  14. A.P. Robertson and W.J. Robertson, Topological vector spaces (Cambridge University Press, Cambridge, 1964).

    MATH  Google Scholar 

  15. R.T. Rockafellar, Convex analysis (Princeton University Press, Princeton, 1970).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dalhousie University, Halifax, Nova Scotia, Canada

    J. M. Borwein

Authors
  1. J. M. Borwein
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

P. Huard

Rights and permissions

Reprints and permissions

Copyright information

© 1979 The Mathematical Programming Society

About this chapter

Cite this chapter

Borwein, J.M. (1979). A multivalued approach to the Farkas lemma. In: Huard, P. (eds) Point-to-Set Maps and Mathematical Programming. Mathematical Programming Studies, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120842

Download citation

  • DOI: https://doi.org/10.1007/BFb0120842

  • Received:

  • Revised:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00797-2

  • Online ISBN: 978-3-642-00798-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation