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Multitime multiobjective variational problems and vector variational-like inequalities

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  • Jayswal, Anurag
  • Singh, Shipra
  • Kurdi, Alia

Abstract

In this paper, we introduce vector variational-like inequality with its weak formulation for multitime multiobjective variational problem. Moreover, we establish the relationships between the solutions of introduced inequalities and (properly) efficient solutions of multitime multiobjective variational problem, involving the invexities of multitime functionals. Some examples are provided to illustrate our results.

Suggested Citation

  • Jayswal, Anurag & Singh, Shipra & Kurdi, Alia, 2016. "Multitime multiobjective variational problems and vector variational-like inequalities," European Journal of Operational Research, Elsevier, vol. 254(3), pages 739-745.
    • Handle: RePEc:eee:ejores:v:254:y:2016:i:3:p:739-745
    DOI: 10.1016/j.ejor.2016.05.006
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    References listed on IDEAS

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    1. Jonathan M. Borwein, 1983. "On the Existence of Pareto Efficient Points," Mathematics of Operations Research, INFORMS, vol. 8(1), pages 64-73, February.
    2. 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.
    3. Ariana Pitea & Mihai Postolache, 2012. "Duality theorems for a new class of multitime multiobjective variational problems," Journal of Global Optimization, Springer, vol. 54(1), pages 47-58, September.
    4. Khurana, Seema, 2005. "Symmetric duality in multiobjective programming involving generalized cone-invex functions," European Journal of Operational Research, Elsevier, vol. 165(3), pages 592-597, September.
    5. S. Al-Homidan & Q. H. Ansari, 2010. "Generalized Minty Vector Variational-Like Inequalities and Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 144(1), pages 1-11, January.
    6. Arana-Jiménez, M. & Ruiz-Garzón, G. & Rufián-Lizana, A. & Osuna-Gómez, R., 2010. "A necessary and sufficient condition for duality in multiobjective variational problems," European Journal of Operational Research, Elsevier, vol. 201(3), pages 672-681, March.
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    Cited by:

    1. Savin Treanţă & Tareq Saeed, 2023. "On Weak Variational Control Inequalities via Interval Analysis," Mathematics, MDPI, vol. 11(9), pages 1-11, May.
    2. Shipra Singh & Aviv Gibali & Simeon Reich, 2021. "Multi-Time Generalized Nash Equilibria with Dynamic Flow Applications," Mathematics, MDPI, vol. 9(14), pages 1-23, July.
    3. Shipra Singh & Aviv Gibali & Simeon Reich, 2024. "Multidimensional Evolution Effects on Non-Cooperative Strategic Games," Mathematics, MDPI, vol. 12(16), pages 1-30, August.

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