Skip to main content
Log in

Characterization of solutions of multiobjective optimization problem

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

Abstract

A characterization of weakly efficient, efficient and properly efficient solutions of multiobjective optimization problems is given in terms of a scalar optimization problem by using a special “distance” function. The concept of the well-posedness for this special scalar problem is then linked with the properly efficient solutions of the multiobjective problem.

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. Amahroq T., Taa A,On Lagrange-Kuhnn-Tucker Multipliers for Multiobjective Optimization Problems, Optimization,41 (1997), 159–172.

    Article  MATH  MathSciNet  Google Scholar 

  2. Ciligot-Traivain M.,On Lagrange-Kuhnn-Tucker Multipliers for Pareto Optimization Problem, Numerical Functional Analysis and Optimization,15 (1994), 689–693.

    Article  MathSciNet  Google Scholar 

  3. Clarke F. H.,Optimization and Nonsmooth Analysis, Wiley-Interscience, New York. (1983).

    MATH  Google Scholar 

  4. Dontchev A. L., Zolezzi T.,Well-Posed Optimization Problems, Lecture Notes in Mathematics, Springer Verlag, Berlin.1543 (1993).

    MATH  Google Scholar 

  5. Gong X. H.,Connectedness of Efficient Solutions Sets for Set-Valued Map in Normed Spaces, Journal of Optimization Theory and Application,83 (1994), 83–96.

    Article  MATH  Google Scholar 

  6. Guerraggio A., Molho E., Zaffaroni A.,On The Notion of Proper Efficiency in Vector Optimization, Journal of Optimization Theory and Application,82 (1994), 1–19.

    Article  MATH  MathSciNet  Google Scholar 

  7. Hiriart-Urruty J. B.,Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces, Mathematics of Operations Research,4 (1978), 79–97.

    Article  MathSciNet  Google Scholar 

  8. Luc D. T.,Theory of Vector Optimization, Lecture Notes in Economics and Mathematical Systems, Springer Verlag, Berlin,319 (1989)

    Google Scholar 

  9. Lucchetti R., Revalski, J. (eds.),Recent Developments in Well-posed Variational Problems, Kluwer Academic Publishers, Dordrecht, (1995).

    MATH  Google Scholar 

  10. Nakayama H., Sawaragi Y., Tanino T.,Theory of Multiobjective Optimization, Academic Press Inc., New York and London, (1985).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Miglierina, E. Characterization of solutions of multiobjective optimization problem. Rend. Circ. Mat. Palermo 50, 153–164 (2001). https://doi.org/10.1007/BF02843924

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02843924

Keywords

Navigation