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A graphical characterization of the efficient set for convex multiobjective problems

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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.

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Authors and Affiliations

  1. Department of Applied Economics (Mathematics), Faculty of Economy, University of Málaga, C/Ejido, 6, Málaga, 29071, Spain

    Francisco Ruiz, Lourdes Rey & María del Mar Muñoz

Authors
  1. Francisco Ruiz
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  2. Lourdes Rey
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  3. María del Mar Muñoz
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Correspondence to Francisco Ruiz.

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Ruiz, F., Rey, L. & Muñoz, M.d.M. A graphical characterization of the efficient set for convex multiobjective problems. Ann Oper Res 164, 115–126 (2008). https://doi.org/10.1007/s10479-008-0346-x

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  • DOI: https://doi.org/10.1007/s10479-008-0346-x

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