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Pareto Efficiency Criteria and Duality for Multiobjective Fractional Programming Problems with Equilibrium Constraints on Hadamard Manifolds

Author

Listed:
  • Arnav Ghosh

    (Department of Mathematics, Indian Institute of Technology Patna, Patna 801103, India
    These authors contributed equally to this work.)

  • Balendu Bhooshan Upadhyay

    (Department of Mathematics, Indian Institute of Technology Patna, Patna 801103, India
    These authors contributed equally to this work.)

  • I. M. Stancu-Minasian

    (“Gheorghe Mihoc-Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, 050711 Bucharest, Romania
    These authors contributed equally to this work.)

Abstract

This article deals with multiobjective fractional programming problems with equilibrium constraints in the setting of Hadamard manifolds (abbreviated as MFPPEC). The generalized Guignard constraint qualification (abbreviated as GGCQ) for MFPPEC is presented. Furthermore, the Karush–Kuhn–Tucker (abbreviated as KKT) type necessary criteria of Pareto efficiency for MFPPEC are derived using GGCQ. Sufficient criteria of Pareto efficiency for MFPPEC are deduced under some geodesic convexity hypotheses. Subsequently, Mond–Weir and Wolfe type dual models related to MFPPEC are formulated. The weak, strong, and strict converse duality results are derived relating MFPPEC and the respective dual models. Suitable nontrivial examples have been furnished to demonstrate the significance of the results established in this article. The results derived in the article extend and generalize several notable results previously existing in the literature. To the best of our knowledge, optimality conditions and duality for MFPPEC have not yet been studied in the framework of manifolds.

Suggested Citation

  • Arnav Ghosh & Balendu Bhooshan Upadhyay & I. M. Stancu-Minasian, 2023. "Pareto Efficiency Criteria and Duality for Multiobjective Fractional Programming Problems with Equilibrium Constraints on Hadamard Manifolds," Mathematics, MDPI, vol. 11(17), pages 1-28, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3649-:d:1223602
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    References listed on IDEAS

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    1. Balendu Bhooshan Upadhyay & Arnav Ghosh, 2023. "On Constraint Qualifications for Mathematical Programming Problems with Vanishing Constraints on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 1-35, October.
    2. M.L. Flegel & C. Kanzow, 2005. "Abadie-Type Constraint Qualification for Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 124(3), pages 595-614, March.
    3. Savin Treanţă & Balendu Bhooshan Upadhyay & Arnav Ghosh & Kamsing Nonlaopon, 2022. "Optimality Conditions for Multiobjective Mathematical Programming Problems with Equilibrium Constraints on Hadamard Manifolds," Mathematics, MDPI, vol. 10(19), pages 1-20, September.
    4. Savin Treanţă & Priyanka Mishra & Balendu Bhooshan Upadhyay, 2022. "Minty Variational Principle for Nonsmooth Interval-Valued Vector Optimization Problems on Hadamard Manifolds," Mathematics, MDPI, vol. 10(3), pages 1-15, February.
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