Skip to main content
SpringerLink
Log in

Monotonic analysis over ordered topological vector spaces: IV

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

In this paper, we present an extension for non-negative increasing and co-radiant (ICR) functions over a topological vector space. We characterize the essential results of abstract convexity such as support set, subdifferential and polarity of these functions. We also give some characterizations of a certain kind of polarity and separation property for non-convex radiant and co-radiant sets.

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. Abasov T.M., Rubinov A.M.: Subdifferential of some classes of non-smooth functions. In: Demyanov, V.F.(eds) Mathematical Models of Analysis of Non-smooth Models, St. Petersburg University Press, Russia (1996)

    Google Scholar 

  2. Doagooei, A.R., Mohebi, H.: Monotonic analysis over ordered topological vector spaces: III (to appear)

  3. Dutta J., Martinez-Legaz J.E., Rubinov A.M.: Monotonic analysis over cones: I. Optimization 53, 165–177 (2004a)

    Article  Google Scholar 

  4. Dutta J., Martinez-Legaz J.E., Rubinov A.M.: Monotonic analysis over cones: II. Optimization 53, 529–547 (2004b)

    Article  Google Scholar 

  5. Dutta J., Martinez-Legaz J.E., Rubinov A.M.: Monotonic analysis over cones: III. J. Convex Anal. 15, 581–592 (2008)

    Google Scholar 

  6. Martinez-Legaz J.E., Rubinov A.M., Schaible S.: Increasing quasi-concave co-adiant functions with applications in mathematical economics. Math. Methods Operation Res. 61, 261–280 (2005)

    Article  Google Scholar 

  7. Mohebi H., Sadeghi H.: Monotonic analysis over non-convex cones. Numer. Funct. Anal. Optim. 26(7&8), 879–895 (2005)

    Article  Google Scholar 

  8. Mohebi H., Sadeghi H.: Monotonic analysis over ordered topological vector spaces: I. Optimization 56(3), 305–321 (2007)

    Article  Google Scholar 

  9. Pallaschke D., Rolewicez S.: Foundations of Mathematical Optimization (Convex Analysis without Linearity). Kluwer Academic Publishers, Boston, Dordrecht, London (1997)

    Google Scholar 

  10. Rockafellar R.T.: Convex Analysis. Princeton University Press, Princeton, NJ (1970)

    Google Scholar 

  11. Rubinov A.M.: Abstract Convexity and Global Optimization. Kluwer Academic Publishers, Boston, Dordrecht, London (2000)

    Google Scholar 

  12. Singer I.: Abstract Convex Analysis. Wiley-Interscience, New York (1997)

    Google Scholar 

  13. Zaffaroni A.: Superlinear Separation of Radiant and Co-radiant Sets. Optimization 56(1& 2), 267–285 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran

    A. R. Doagooei & Hossein Mohebi

Authors
  1. A. R. Doagooei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hossein Mohebi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hossein Mohebi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Doagooei, A.R., Mohebi, H. Monotonic analysis over ordered topological vector spaces: IV. J Glob Optim 45, 355–369 (2009). https://doi.org/10.1007/s10898-008-9379-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-008-9379-6

Keywords

Mathematics Subject Classification (2000)

Search

Navigation