About duality and alternative in multiobjective optimization

  • D. T. Luc
Technical Note

Abstract

McLinden's result on the equivalence between a theorem of the alternative and a duality theorem for constrained optimization problems is extended to the multiobjective case. We then discuss some existing results on that topic and present an alternative approach to duality relations in conditionally complete lattices.

Key Words

Duality theorem relations of the alternative domaination property 

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References

  1. 1.
    McLinden, L.,Duality Theorems and Theorems of the Alternative, Proceedings of the American Mathematical Society, Vol. 5, pp. 172–175, 1975.Google Scholar
  2. 2.
    Rosinger, E. E.,Duality and Alternative in Multiobjective Optimization, Proceedings of the American Mathematical Society, Vol. 64, pp. 307–312, 1977.Google Scholar
  3. 3.
    Luc, D. T.,On Duality Theory in Multiobjective Programming, Journal of Optimization Theory and Applications, Vol. 43, pp. 557–582, 1984.Google Scholar
  4. 4.
    Azimov, A. Ja.,Duality in Vector Optimization Problems, Soviet Mathematics Doklady, Vol. 26, pp. 170–174, 1982.Google Scholar

Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • D. T. Luc
    • 1
  1. 1.Computer and Automation InstituteHungarian Academy of SciencesBudapestHungary

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