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Lagrangian Duality for Multiobjective Programming Problems in Lexicographic Order

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  • X. F. Hu
  • L. N. Wang

Abstract

This paper deals with a constraint multiobjective programming problem and its dual problem in the lexicographic order. We establish some duality theorems and present several existence results of a Lagrange multiplier and a lexicographic saddle point theorem. Meanwhile, we study the relations between the lexicographic saddle point and the lexicographic solution to a multiobjective programming problem.

Suggested Citation

  • X. F. Hu & L. N. Wang, 2013. "Lagrangian Duality for Multiobjective Programming Problems in Lexicographic Order," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:573408
    DOI: 10.1155/2013/573408
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    References listed on IDEAS

    as
    1. W. Song, 1997. "Lagrangian Duality for Minimization of Nonconvex Multifunctions," Journal of Optimization Theory and Applications, Springer, vol. 93(1), pages 167-182, April.
    2. Peter C. Fishburn, 1974. "Exceptional Paper--Lexicographic Orders, Utilities and Decision Rules: A Survey," Management Science, INFORMS, vol. 20(11), pages 1442-1471, July.
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