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Introducing Nonpolyhedral Cones to Multiobjective Programming

In: Multiobjective Programming and Goal Programming

Author

Listed:
  • Alexander Engau

    (University of Waterloo)

  • Margaret M. Wiecek

    (Clemson University)

Abstract

The nondominated set of a multiobjective program is investigated with respect to a class of nonpolyhedral cones, that are defined in direct generalization of Pareto, polyhedral, second order and general p-th order cones. Properties of these cones are derived using the concept of positively homogeneous functions, and two approaches to generating the associated nondominated points are presented. In Particular, it is shown how a well known relationship between the nondominated points with respect to a polyhedral cone and Pareto points can be generalized for a non-polyhedral cone. In addition, several scalarization methods that have originally been formulated for finding Pareto points can be modified to also allow for a general (polyhedral or nonpolyhedral) cone. The results are illustrated on examples and discussed for a specific class of nonpolyhedral cones.

Suggested Citation

  • Alexander Engau & Margaret M. Wiecek, 2009. "Introducing Nonpolyhedral Cones to Multiobjective Programming," Lecture Notes in Economics and Mathematical Systems, in: Vincent Barichard & Matthias Ehrgott & Xavier Gandibleux & Vincent T'Kindt (ed.), Multiobjective Programming and Goal Programming, pages 35-45, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-85646-7_4
    DOI: 10.1007/978-3-540-85646-7_4
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    Cited by:

    1. Stephan Dempe & Gabriele Eichfelder & Jörg Fliege, 2015. "On the effects of combining objectives in multi-objective optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(1), pages 1-18, August.

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