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

Author

Listed:
  • 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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