# 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

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topRadu 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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