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A graphical characterization of the efficient set for convex multiobjective problems

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  • Francisco Ruiz
  • Lourdes Rey
  • María Muñoz

Abstract

In this paper, a graphical characterization, in the decision space, of the properly efficient solutions of a convex multiobjective problem is derived. This characterization takes into account the relative position of the gradients of the objective functions and the active constraints at the given feasible solution. The unconstrained case with two objective functions and with any number of functions and the general constrained case are studied separately. In some cases, these results can provide a visualization of the efficient set, for problems with two or three variables. Besides, a proper efficiency test for general convex multiobjective problems is derived, which consists of solving a single linear optimization problem. Copyright Springer Science+Business Media, LLC 2008

Suggested Citation

  • Francisco Ruiz & Lourdes Rey & María Muñoz, 2008. "A graphical characterization of the efficient set for convex multiobjective problems," Annals of Operations Research, Springer, vol. 164(1), pages 115-126, November.
    • Handle: RePEc:spr:annopr:v:164:y:2008:i:1:p:115-126:10.1007/s10479-008-0346-x
    DOI: 10.1007/s10479-008-0346-x
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    References listed on IDEAS

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    1. T. J. Lowe & J.-F. Thisse & J. E. Ward & R. E. Wendell, 1984. "On Efficient Solutions to Multiple Objective Mathematical Programs," Management Science, INFORMS, vol. 30(11), pages 1346-1349, November.
    2. James Ward, 1989. "Structure of Efficient Sets for Convex Objectives," Mathematics of Operations Research, INFORMS, vol. 14(2), pages 249-257, May.
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