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Lagrangian function and duality theory in multiobjective programming with set functions

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Abstract

Using the concept of vector-valued Lagrangian functions, we characterize a special class of solutions,D-solutions, of a multiobjective programming problem with set functions in which the domination structure is described by a closed convex coneD. Properties of two perturbation functions, primal map and dual map, are also studied. Results lead to a general duality theorem.

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Authors and Affiliations

  1. Department of Mathematics, University of Alabama, Tuscaloosa, Alabama

    W. S. Hsia (Professor) & T. Y. Lee (Assistant Professor)

Authors
  1. W. S. Hsia
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  2. T. Y. Lee
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Additional information

Communicated by B. R. Agins

The authors greatly appreciate helpful and valuable comments and suggestions received from the referee.

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Hsia, W.S., Lee, T.Y. Lagrangian function and duality theory in multiobjective programming with set functions. J Optim Theory Appl 57, 239–251 (1988). https://doi.org/10.1007/BF00938538

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  • DOI: https://doi.org/10.1007/BF00938538

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