Skip to main content
Log in

On Efficient Solutions in Vector Optimization

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

Abstract

A new characterization is obtained for the existence of an efficient solution of a vector optimization problem in terms of associated scalar optimization problems. The consequences for linear vector optimization problems are derived as a special case, Applications to convex vector optimization problems are also discussed.

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. Borwein, J. M., On the Existence of Pareto Efficient Points, Mathematics of Operations Research, Vol. 8, pp. 64–73, 1983.

    Google Scholar 

  2. Sawaragi, Y., Nakayama, H., and Tanino, T., Theory of Multiobjective Optimization, Academic Press, New York, New York, 1985.

    Google Scholar 

  3. Henig, M. I., Existence and Characterization of Efficient Decisions with Respect to Cones, Mathematical Programming, Vol. 23, pp. 111–116, 1982.

    Google Scholar 

  4. Bitran, G. R., and Magnanti, T. L., The Structure of Admissible Points with Respect to Cone Dominance, Journal of Optimization Theory and Applications, Vol. 29, pp. 573–614, 1979.

    Google Scholar 

  5. Ruiz-Canales, P., and Rufian-Lizana, A., A Characterization of Weakly Efficient Points, Mathematical Programming, Vol. 68, pp. 205–212, 1995.

    Google Scholar 

  6. Rockafellar, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.

    Google Scholar 

  7. Hiriart-Urruty, J. B., and Lemarechal, C., Convex Analysis and Minimization Algorithms, Vol. 1, Springer Verlag, Berlin, Germany, 1993.

    Google Scholar 

  8. Deng, S., Characterizations of the Nonemptiness and Compactness of Solution Sets in Convex Vector Optimization, Journal of Optimization Theory and Applications, Vol. 96, pp. 123–131, 1998.

    Google Scholar 

  9. Cheng, G. Y. and Craven, B. D., Existence and Continuity of Solutions for Vector Optimization, Journal of Optimization Theory and Applications, Vol. 81, pp. 459–467, 1994.

    Google Scholar 

  10. Deng, S., On Approximate Solutions in Convex Vector Optimization, SIAM Journal on Control and Optimization, Vol. 35, pp. 2128–2136, 1997.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Deng, S. On Efficient Solutions in Vector Optimization. Journal of Optimization Theory and Applications 96, 201–209 (1998). https://doi.org/10.1023/A:1022627520279

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022627520279

Navigation