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Weak efficiency in multiobjective variational problems under generalized convexity

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Abstract

In this paper, we provide new pseudoinvexity conditions on the involved functionals of a multiobjective variational problem, such that all vector Kuhn-Tucker or Fritz John points are weakly efficient solutions if and only if these conditions are fulfilled. We relate weakly efficient solutions to optimal solutions of weighting problems. We improve recent papers, and we generalize pseudoinvexity conditions used in multiobjective mathematical programming, so as some of their characterization results. The new conditions and results are illustrated with an example.

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Authors and Affiliations

  1. Departamento de Estadística e I.O., Facultad de CCSS y de la Comunicación, Universidad de Cádiz, Avda. de la Universidad s/n, 11402, Jerez de la Frontera, Cádiz, Spain

    M. Arana-Jiménez & G. Ruiz-Garzón

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

    A. Rufián-Lizana & R. Osuna-Gómez

Authors
  1. M. Arana-Jiménez
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  2. G. Ruiz-Garzón
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  3. A. Rufián-Lizana
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  4. R. Osuna-Gómez
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Corresponding author

Correspondence to M. Arana-Jiménez.

Additional information

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

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Arana-Jiménez, M., Ruiz-Garzón, G., Rufián-Lizana, A. et al. Weak efficiency in multiobjective variational problems under generalized convexity. J Glob Optim 52, 109–121 (2012). https://doi.org/10.1007/s10898-011-9689-y

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  • DOI: https://doi.org/10.1007/s10898-011-9689-y

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