Advertisement

On duality theory in multiobjective programming

  • D. T. Luc
Contributed Papers

Abstract

In this paper, we study different vector-valued Lagrangian functions and we develop a duality theory based upon these functions for nonlinear multiobjective programming problems. The saddle-point theorem and the duality theorem are derived for these problems under appropriate convexity assumptions. We also give some relationships between multiobjective optimizations and scalarized problems. A duality theory obtained by using the concept of vector-valued conjugate functions is discussed.

Key Words

Lagrangian functions M-convexity saddle points Slater's constraint qualification dual functions conjugate functions 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Tanino, T., andSawaragi, Y.,Duality Theory in Multiobjective Programming, Journal of Optimization Theory and Applications, Vol. 27, pp. 509–529, 1979.Google Scholar
  2. 2.
    Tanino, T., andSawaragi, Y.,Conjugate Maps and Duality in Multiobjective Optimization, Journal of Optimization Theory and Applications, Vol. 31, pp. 473–479, 1980.Google Scholar
  3. 3.
    Bitran, G. R.,Duality for Nonlinear Multiple-Criteria Optimization Problems, Journal of Optimization Theory and Applications, Vol. 35, pp. 367–401, 1981.Google Scholar
  4. 4.
    Corley, H. W.,Duality Theory for Maximizations with Respect to Cones, Journal of Mathematical Analysis and Applications, Vol. 84, pp. 560–568, 1981.Google Scholar
  5. 5.
    Rockafellar, T. R.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.Google Scholar
  6. 6.
    Luenberger, D. G.,Optimization by Vector Space Methods, Wiley, New York, New York, 1969.Google Scholar
  7. 7.
    Luc, D. T.,M-Optimality and Dynamic Programming (to appear).Google Scholar

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

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

Personalised recommendations