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Duality and Weak Efficiency in Vector Variational Problems

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Abstract

We establish weak, strong, and converse duality results for weakly efficient solutions in vector or multiobjective variational problems, which extend and improve recent papers. For this purpose, we consider Kuhn–Tucker optimality conditions, weighting variational problems, and some classes of generalized convex functions, recently introduced, which are extended in this work. Furthermore, a related open question is discussed.

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Acknowledgements

This work was partially supported by Ministerio de Economía y Competitividad, under grants MTM2010-15383 and MTM2010-16401 with the participation of FEDER, and Consejería de Educación y Ciencia de la Junta de Andalucía, research groups FQM-243 and FQM-315.

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Authors and Affiliations

  1. Department of Statistics and Operational Research, Faculty of SSCC and Communication, University of Cádiz, 11405, Jerez de la Frontera, Spain

    M. Arana Jiménez

  2. Department of Mathematics, Faculty of Sciences, University of Cádiz, 11510, Puerto Real, Spain

    F. Ortegón Gallego

Authors
  1. M. Arana Jiménez
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  2. F. Ortegón Gallego
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Correspondence to M. Arana Jiménez.

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Arana Jiménez, M., Ortegón Gallego, F. Duality and Weak Efficiency in Vector Variational Problems. J Optim Theory Appl 159, 547–553 (2013). https://doi.org/10.1007/s10957-013-0333-5

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  • DOI: https://doi.org/10.1007/s10957-013-0333-5

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