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On Quasiconvex Multiobjective Optimization and Variational Inequalities Using Greenberg–Pierskalla Based Generalized Subdifferentials

Author

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  • Shashi Kant Mishra

    (Banaras Hindu University)

  • Vivek Laha

    (Banaras Hindu University)

  • Mohd Hassan

    (University of Ladakh, Leh Campus)

Abstract

In this paper, we first characterize generalized convex functions introduced by Linh and Penot Optimization (62: 943–959, 2013) by using generalized monotonicity of the generalized subdifferentials. We use vector variational inequalities in terms of generalized subdifferentials to identify efficient solutions of a multiobjective optimization problem involving quasiconvex functions. We also establish the Minty variational principle by utilizing the mean value theorem established by Kabgani and Soleimani-damaneh (Numer. Funct. Anal. Optim 38: 1548–1563, 2017) for quasiconvex functions in terms of Greenberg–Pierskalla subdifferentials.

Suggested Citation

  • Shashi Kant Mishra & Vivek Laha & Mohd Hassan, 2024. "On Quasiconvex Multiobjective Optimization and Variational Inequalities Using Greenberg–Pierskalla Based Generalized Subdifferentials," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 1169-1186, September.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:3:d:10.1007_s10957-024-02505-3
    DOI: 10.1007/s10957-024-02505-3
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    References listed on IDEAS

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    1. Q. H. Ansari & G. M. Lee, 2010. "Nonsmooth Vector Optimization Problems and Minty Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 1-16, April.
    2. Qamrul Ansari & Mahboubeh Rezaie & Jafar Zafarani, 2012. "Generalized vector variational-like inequalities and vector optimization," Journal of Global Optimization, Springer, vol. 53(2), pages 271-284, June.
    3. S. K. Mishra & Vivek Laha, 2013. "On Approximately Star-Shaped Functions and Approximate Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 278-293, February.
    4. Satoshi Suzuki & Daishi Kuroiwa, 2015. "Characterizations of the solution set for quasiconvex programming in terms of Greenberg–Pierskalla subdifferential," Journal of Global Optimization, Springer, vol. 62(3), pages 431-441, July.
    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. Yogendra Pandey & S. K. Mishra, 2018. "Optimality conditions and duality for semi-infinite mathematical programming problems with equilibrium constraints, using convexificators," Annals of Operations Research, Springer, vol. 269(1), pages 549-564, October.
    7. Yogendra Pandey & Shashi Kant Mishra, 2016. "Duality for Nonsmooth Optimization Problems with Equilibrium Constraints, Using Convexificators," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 694-707, November.
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