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Duality in nonconvex vector optimization

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Abstract

In this paper, duality relations in nonconvex vector optimization are studied. An augmented Lagrangian function associated with the primal problem is introduced and efficient solutions to the given vector optimization problem, are characterized in terms of saddle points of this Lagrangian. The dual problem to the given primal one, is constructed with the help of the augmented Lagrangian introduced and weak and strong duality theorems are proved. Illustrative examples for duality relations are provided.

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Authors and Affiliations

  1. Department of Industrial Engineering, Eskisehir Technical University, Iki Eylul Campus, Eskisehir, 26555, Turkey

    Refail Kasimbeyli

  2. Department of Optimization, Mehrgan Niro Pouya Company, Kermanshah, Iran

    Masoud Karimi

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  1. Refail Kasimbeyli
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  2. Masoud Karimi
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Correspondence to Refail Kasimbeyli.

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The author published under the name Rafail N. Gasimov until 2007.

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Kasimbeyli, R., Karimi, M. Duality in nonconvex vector optimization. J Glob Optim 80, 139–160 (2021). https://doi.org/10.1007/s10898-021-01018-x

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