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Multi-objective semi-infinite variational problem and generalized invexity

Author

Listed:
  • Promila Kumar

    (University of Delhi)

  • Bharti Sharma

    (University of Delhi)

  • Jyoti Dagar

    (University of Delhi)

Abstract

In this paper, multiobjective semi-infinite variational problem (MSVP) has been considered. Relationship between efficiency, vector Kuhn Tucker point and vector Fritz John point for the stated problem have been established and authenticated by means of examples. Two duals namely Wolfe and Mond–Weir are purposed for (MSVP) and duality results are established under generalized invexity assumptions. Efficient solution of (MSVP) has been characterized by vector saddle point of a vector valued Lagrangian function of (MSVP). An equivalent (MSVP) is also constructed by a suitable modification of the objective function.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:opsear:v:54:y:2017:i:3:d:10.1007_s12597-016-0293-2
    DOI: 10.1007/s12597-016-0293-2
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    References listed on IDEAS

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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. Lopez, Marco & Still, Georg, 2007. "Semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 180(2), pages 491-518, July.
    3. Tadeusz Antczak, 2014. "On efficiency and mixed duality for a new class of nonconvex multiobjective variational control problems," Journal of Global Optimization, Springer, vol. 59(4), pages 757-785, August.
    4. 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.
    5. Tadeusz Antczak, 2015. "Sufficient optimality criteria and duality for multiobjective variational control problems with $$G$$ G -type I objective and constraint functions," Journal of Global Optimization, Springer, vol. 61(4), pages 695-720, April.
    6. 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.
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