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Duality and a Characterization of Pseudoinvexity for Pareto and Weak Pareto Solutions in Nondifferentiable Multiobjective Programming

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Abstract

In this paper, we unify recent optimality results under directional derivatives by the introduction of new pseudoinvex classes of functions, in relation to the study of Pareto and weak Pareto solutions for nondifferentiable multiobjective programming problems. We prove that in order for feasible solutions satisfying Fritz John conditions to be Pareto or weak Pareto solutions, it is necessary and sufficient that the nondifferentiable multiobjective problem functions belong to these classes of functions, which is illustrated by an example. We also study the dual problem and establish weak, strong, and converse duality results.

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Acknowledgements

This work was partially supported by the grant MTM2010-15383 of the Science and Education Spanish Ministry.

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Authors and Affiliations

  1. Departamento de Estadística e I.O., Facultad de Ciencias Sociales y de la Comunicación, Universidad de Cádiz, 11405, Jerez de la Frontera, Spain

    M. Arana-Jiménez & G. Ruiz-Garzón

  2. Departamento de Estadística e I.O., Universidad de Sevilla, Sevilla, Spain

    R. Osuna-Gómez

  3. Departamento de Economía, Métodos Cuantitativos e H. Económica, Universidad Pablo de Olavide, Seville, Spain

    B. Hernández-Jiménez

Authors
  1. M. Arana-Jiménez
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  2. G. Ruiz-Garzón
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  3. R. Osuna-Gómez
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  4. B. Hernández-Jiménez
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Corresponding author

Correspondence to M. Arana-Jiménez.

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Communicated by Byung-Soo Lee.

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Arana-Jiménez, M., Ruiz-Garzón, G., Osuna-Gómez, R. et al. Duality and a Characterization of Pseudoinvexity for Pareto and Weak Pareto Solutions in Nondifferentiable Multiobjective Programming. J Optim Theory Appl 156, 266–277 (2013). https://doi.org/10.1007/s10957-012-0123-5

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  • DOI: https://doi.org/10.1007/s10957-012-0123-5

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