Comparison between different duals in multiobjective fractional programming

Radu Boţ; Robert Chares; Gert Wanka

Open Mathematics (2007)

  • Volume: 5, Issue: 3, page 452-469
  • ISSN: 2391-5455

Abstract

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The present paper is a continuation of [2] where we deal with the duality for a multiobjective fractional optimization problem. The basic idea in [2] consists in attaching an intermediate multiobjective convex optimization problem to the primal fractional problem, using an approach due to Dinkelbach ([6]), for which we construct then a dual problem expressed in terms of the conjugates of the functions involved. The weak, strong and converse duality statements for the intermediate problems allow us to give dual characterizations for the efficient solutions of the initial fractional problem. The aim of this paper is to compare the intermediate dual problem with other similar dual problems known from the literature. We completely establish the inclusion relations between the image sets of the duals as well as between the sets of maximal elements of the image sets.

How to cite

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Radu Boţ, Robert Chares, and Gert Wanka. "Comparison between different duals in multiobjective fractional programming." Open Mathematics 5.3 (2007): 452-469. <http://eudml.org/doc/269675>.

@article{RaduBoţ2007,
abstract = {The present paper is a continuation of [2] where we deal with the duality for a multiobjective fractional optimization problem. The basic idea in [2] consists in attaching an intermediate multiobjective convex optimization problem to the primal fractional problem, using an approach due to Dinkelbach ([6]), for which we construct then a dual problem expressed in terms of the conjugates of the functions involved. The weak, strong and converse duality statements for the intermediate problems allow us to give dual characterizations for the efficient solutions of the initial fractional problem. The aim of this paper is to compare the intermediate dual problem with other similar dual problems known from the literature. We completely establish the inclusion relations between the image sets of the duals as well as between the sets of maximal elements of the image sets.},
author = {Radu Boţ, Robert Chares, Gert Wanka},
journal = {Open Mathematics},
keywords = {multiobjective fractional programming; Fenchel duality; Fenchel-Lagrange duality; maximal elements; properly efficient elements},
language = {eng},
number = {3},
pages = {452-469},
title = {Comparison between different duals in multiobjective fractional programming},
url = {http://eudml.org/doc/269675},
volume = {5},
year = {2007},
}

TY - JOUR
AU - Radu Boţ
AU - Robert Chares
AU - Gert Wanka
TI - Comparison between different duals in multiobjective fractional programming
JO - Open Mathematics
PY - 2007
VL - 5
IS - 3
SP - 452
EP - 469
AB - The present paper is a continuation of [2] where we deal with the duality for a multiobjective fractional optimization problem. The basic idea in [2] consists in attaching an intermediate multiobjective convex optimization problem to the primal fractional problem, using an approach due to Dinkelbach ([6]), for which we construct then a dual problem expressed in terms of the conjugates of the functions involved. The weak, strong and converse duality statements for the intermediate problems allow us to give dual characterizations for the efficient solutions of the initial fractional problem. The aim of this paper is to compare the intermediate dual problem with other similar dual problems known from the literature. We completely establish the inclusion relations between the image sets of the duals as well as between the sets of maximal elements of the image sets.
LA - eng
KW - multiobjective fractional programming; Fenchel duality; Fenchel-Lagrange duality; maximal elements; properly efficient elements
UR - http://eudml.org/doc/269675
ER -

References

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  4. [4] R.I. Boţ and G. Wanka: “An analysis of some dual problems in multiobjective optimization (II)/rd, Optimization, Vol. 53, (2004), pp. 301–324. http://dx.doi.org/10.1080/02331930410001715523 Zbl1144.90474
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  12. [12] R.T. Rockafellar: Convex analysis, Princeton University Press, 1970. 
  13. [13] G. Wanka and R.I. Boţ: “A new duality approach for multiobjective convex optimization problems/rd, J. Nonlinear and Convex Anal., Vol. 3, (2002), pp. 41–57. Zbl1007.90056
  14. [14] G. Wanka and R.I. Boţ: “On the relations between different dual problems in convex mathematical programming/rd, In: P. Chamoni and R. Leisten and A. Martin and J. Minnemann and A. Stadler (Eds.), Operations Research Proceedings 2001, Springer-Verlag, Berlin, 2002, pp. 255–265. 
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