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Duality and Weak Efficiency in Vector Variational Problems

Author

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  • M. Arana Jiménez

    (University of Cádiz)

  • F. Ortegón Gallego

    (University of Cádiz)

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.

Suggested Citation

  • M. Arana Jiménez & F. Ortegón Gallego, 2013. "Duality and Weak Efficiency in Vector Variational Problems," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 547-553, November.
    • Handle: RePEc:spr:joptap:v:159:y:2013:i:2:d:10.1007_s10957-013-0333-5
    DOI: 10.1007/s10957-013-0333-5
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    References listed on IDEAS

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    1. M. Arana-Jiménez & G. Ruiz-Garzón & A. Rufián-Lizana & R. Osuna-Gómez, 2012. "Weak efficiency in multiobjective variational problems under generalized convexity," Journal of Global Optimization, Springer, vol. 52(1), pages 109-121, January.
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    Cited by:

    1. Promila Kumar & Bharti Sharma & Jyoti Dagar, 2017. "Multi-objective semi-infinite variational problem and generalized invexity," OPSEARCH, Springer;Operational Research Society of India, vol. 54(3), pages 580-597, September.
    2. Promila Kumar & Bharti Sharma, 2016. "Weak efficiency of higher order for multiobjective fractional variational problem," OPSEARCH, Springer;Operational Research Society of India, vol. 53(3), pages 538-552, September.

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    1. Promila Kumar & Bharti Sharma, 2016. "Weak efficiency of higher order for multiobjective fractional variational problem," OPSEARCH, Springer;Operational Research Society of India, vol. 53(3), pages 538-552, September.
    2. Promila Kumar & Bharti Sharma & Jyoti Dagar, 2017. "Multi-objective semi-infinite variational problem and generalized invexity," OPSEARCH, Springer;Operational Research Society of India, vol. 54(3), pages 580-597, September.

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