Skip to main content
Log in

Efficiency and Generalized Concavity

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

In a recent paper on multiobjective maximization problems (Ref. 1), the authors use explicit quasiconcavity of the objective functions to prove a characterization of weakly efficient solutions and local-global properties. We provide results which are stronger in part and are derived with shorter proofs. We also present additional results.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. RUÍZ-CANALES, P., and RUFIÁN-LIZANA, A., A Characterization of Weakly Efficient Points, Mathematical Programming, Vol. 68, pp. 205–212, 1995.

    Google Scholar 

  2. CHANKONG, V., and HAINES, Y., Multiobjective Decision Making: Theory and Methodology, North-Holland, Amsterdam, Netherlands, 1983.

    Google Scholar 

  3. JAHN, J., Mathematical Vector Optimization in Partially Ordered Linear Spaces, Peter Lang Verlag, Frankfurt, Germany, 1986.

    Google Scholar 

  4. LUC, D. T., Theory of Vector Optimization, Springer Verlag, Berlin, Germany, 1989.

    Google Scholar 

  5. SAWARAGI, Y., NAKAYAMA, H., and TANINO, T., Theory of Multiobjective Optimization, Academic Press, New York, New York, 1985.

    Google Scholar 

  6. CHOO, E. U., Multicriteria Linear Fractional Programming, PhD Thesis, University of British Columbia, Vancouver, British Columbia, Canada, 1980.

  7. SCHAIBLE, S., Bicriteria Quasiconcave Programs, Cahiers du Centre d'Études de Recherche Opérationelle, Vol. 25, pp. 93–101, 1983.

    Google Scholar 

  8. CHOO, E. U., SCHAIBLE, S., and CHEW, K. P., Connectedness of the Efficient Set in Three-Criteria Quasiconcave Programming, Cahiers du Centre d'Études de Recherche Opérationelle, Vol. 27, pp. 213–220, 1985.

    Google Scholar 

  9. DANIILIDIS, A., HADJISAVVAS, N., and SCHAIBLE, S., Connectedness of the Efficient Set for Three-Objective Quasiconcave Maximization Problems, Journal of Optimization Theory and Applications, Vol. 93, pp. 517–524, 1997.

    Google Scholar 

  10. AVRIEL, M., DIEWERT, W. E., SCHAIBLE, S., and ZANG, I., Generalized Concavity, Plenum Publishing Corporation, New York, New York, 1988.

    Google Scholar 

  11. LUC, D. T., On Three Concepts of Quasiconvexity in Vector Optimization, Acta Mathematica Vietnamica, Vol. 15, pp. 3–9, 1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Luc, D.T., Schaible, S. Efficiency and Generalized Concavity. Journal of Optimization Theory and Applications 94, 147–153 (1997). https://doi.org/10.1023/A:1022663804177

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022663804177

Navigation