Skip to main content
Log in

Approximation in multiobjective optimization

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

Abstract

Some results of approximation type for multiobjective optimization problems with a finite number of objective functions are presented. Namely, for a sequence of multiobjective optimization problems P n which converges in a suitable sense to a limit problem P, properties of the sequence of approximate Pareto efficient sets of the P n 's, are studied with respect to the Pareto efficient set of P. The exterior penalty method as well as the variational approximation method appear to be particular cases of this framework.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aubin, J. P. (1979), Mathematical Methods of Game and Economic Theory, North Holland Publ. Amsterdam.

    Google Scholar 

  2. Attouch, H. (1984), Variational Convergence for Functions and Operators, Pitman Advanced Publishing Program, Boston-London-Melbourne.

    Google Scholar 

  3. Aze, D. and J. P., Penot (1987), Operations on Convergent Families of Sets and Functions, Publication AVAMAC, Université de Perpignan, France, no. 87–05, Vol. 1.

    Google Scholar 

  4. Céa, J. (1971), Optimisation, théorie et algorithmes, Dunod.

  5. Dugośiia, D. P. and M. D., Aśić (1986), Uniform Convergence and Pareto Optimality, Optimization 17 (6), 723–729.

    Google Scholar 

  6. Karlin, S. (1960), Mathematical Methods and Theory in Games, Programming and Economics, Vol. I, McGraw Hill, New York.

    Google Scholar 

  7. Kutateladze, S. S. (1979), Convex ε-Programming, Soviet Mathematical Doklady 20, 391–393.

    Google Scholar 

  8. Lemaire, B. (1988), Coupling Optimization Methods and Variational Convergence, International Series of Numerical Mathematics, Vol. 84(c), Birkhäuser Verlag, pp. 163–179.

  9. Lemaire, B. (1987), Convergence in Vector Optimization. Communication at the Congrès Franco-Québécois d' Analyse Non-Linéaire, Perpignan, France.

  10. Vály, István (1987), Epsilon Solutions and Duality in Vector Optimization, Working paper WP-87–43. Institute for Applied Systems Analysis. Laxenbourg, Austria.

    Google Scholar 

  11. White, D. J. (1984), Multiobjective Programming and Penalty Functions, JOTA 43 (4), 583–599.

    Google Scholar 

  12. White, D. J. (1986), Epsilon Efficiency, Journal of Optimization Theory and Application 49 (2), 319–337.

    Google Scholar 

  13. Zangwill, W. I. (1969), Nonlinear Programming, Prentice-Hall, Englewood Cliffs, New Jersey.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lemaire, B. Approximation in multiobjective optimization. J Glob Optim 2, 117–132 (1992). https://doi.org/10.1007/BF00122049

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00122049

Key words

AMS subject classifications (1991)

Navigation