Multiobjective duality for convex ratios

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Abstract

In this paper we present a duality approach for a multiobjective fractional programming problem. The components of the vector objective function are particular ratios involving the square of a convex function and a positive concave function. Applying the Fenchel-Rockafellar duality theory for a scalar optimization problem associated to the multiobjective primal, a dual problem is derived. This scalar dual problem is formulated in terms of conjugate functions and its structure gives an idea about how to construct a multiobjective dual problem in a natural way. Weak and strong duality assertions are presented. © 2002 Elsevier Science (USA). All rights reserved.

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Wanka, G., & Boţ, R. I. (2002). Multiobjective duality for convex ratios. Journal of Mathematical Analysis and Applications, 275(1), 354–368. https://doi.org/10.1016/S0022-247X(02)00361-X

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