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

Author

Listed:
  • M. Arana-Jiménez

    (Universidad de Cádiz)

  • G. Ruiz-Garzón

    (Universidad de Cádiz)

  • R. Osuna-Gómez

    (Universidad de Sevilla)

  • B. Hernández-Jiménez

    (Universidad Pablo de Olavide)

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.

Suggested Citation

  • M. Arana-Jiménez & G. Ruiz-Garzón & R. Osuna-Gómez & B. Hernández-Jiménez, 2013. "Duality and a Characterization of Pseudoinvexity for Pareto and Weak Pareto Solutions in Nondifferentiable Multiobjective Programming," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 266-277, February.
    • Handle: RePEc:spr:joptap:v:156:y:2013:i:2:d:10.1007_s10957-012-0123-5
    DOI: 10.1007/s10957-012-0123-5
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    References listed on IDEAS

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    1. Antczak, Tadeusz, 2002. "Multiobjective programming under d-invexity," European Journal of Operational Research, Elsevier, vol. 137(1), pages 28-36, February.
    2. Suneja, S.K. & Khurana, Seema & Vani, 2008. "Generalized nonsmooth invexity over cones in vector optimization," European Journal of Operational Research, Elsevier, vol. 186(1), pages 28-40, April.
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