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Contingent derivative of the perturbation map in multiobjective optimization

  • D. S. Shi
Contributed Papers

Abstract

Consider a parametrized multiobjective optimization problem with parameteru. LetG(u) be the objective space image of the feasible region, and letW(u)=MinG(u) (the perturbation map) be the efficient set in the objective space. The purpose of this paper is to investigate the relationship between the contingent derivativeDW ofW with respect tou and the contingent derivativeDG ofG with respect tou. Tanino (Ref. 1) proves that MinDGDW under certain conditions. In this paper, we prove that MinDG=MinDW under weaker conditions than Tanino's and that MinDG=DW under certain conditions. The paper does this by introducing a weaker notion of set-valued derivative. Along the way, the paper improves another of Tanino's results by using weaker conditions.

Key Words

Multiobjective optimization contingent derivative perturbation map TP-derivative 

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References

  1. 1.
    Tanino, T.,Sensitivity Analysis in Multiobjective Optimization, Journal of Optimization Theory and Applications, Vol. 56, pp. 479–499, 1988.Google Scholar
  2. 2.
    Aubin, J. P., andEkeland, L.,Applied Nonlinear Analysis, John Wiley, New York, New York, 1984.Google Scholar
  3. 3.
    Yu, P. L.,Cone Convexity, Cone Extreme Points, and Nondominated Solutions in Decision Problems with Multiobjectives, Journal of Optimization Theory and Applications, Vol. 14, pp. 319–377, 1974.Google Scholar
  4. 4.
    Holmes, R. B.,Geometric Functional Analysis and Its Applications, Springer-Verlag, New York, New York, 1975.Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • D. S. Shi
    • 1
  1. 1.Department of Economic MathematicsZhejiang Institute of Finance and EconomicsHangzhouPRC

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