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Constraint Qualifications and Optimality Conditions for Multiobjective Mathematical Programming Problems with Vanishing Constraints on Hadamard Manifolds

Author

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  • Balendu Bhooshan Upadhyay

    (Department of Mathematics, Indian Institute of Technology Patna, Patna 801103, India)

  • Arnav Ghosh

    (Department of Mathematics, Indian Institute of Technology Patna, Patna 801103, India)

  • Savin Treanţă

    (Department of Applied Mathematics, National University of Science and Technology POLITEHNICA Bucharest, 060042 Bucharest, Romania
    Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania
    “Fundamental Sciences Applied in Engineering” Research Center (SFAI), National University of Science and Technology POLITEHNICA Bucharest, 060042 Bucharest, Romania)

  • Jen-Chih Yao

    (Center for General Education, China Medical University, Taichung 40402, Taiwan
    Academy of Romanian Scientists, 050044 Bucharest, Romania)

Abstract

In this paper, we investigate constraint qualifications and optimality conditions for multiobjective mathematical programming problems with vanishing constraints (MOMPVC) on Hadamard manifolds. The MOMPVC-tailored generalized Guignard constraint qualification (MOMPVC-GGCQ) for MOMPVC is introduced in the setting of Hadamard manifolds. By employing MOMPVC-GGCQ and the intrinsic properties of Hadamard manifolds, we establish Karush–Kuhn–Tucker (KKT)-type necessary Pareto efficiency criteria for MOMPVC. Moreover, we introduce several MOMPVC-tailored constraint qualifications and develop interrelations among them. In particular, we establish that the MOMPVC-tailored constraint qualifications introduced in this paper turn out to be sufficient conditions for MOMPVC-GGCQ. Suitable illustrative examples are furnished in the framework of well-known Hadamard manifolds to validate and demonstrate the importance and significance of the derived results. To the best of our knowledge, this is the first time that constraint qualifications, their interrelations, and optimality criteria for MOMPVC have been explored in the framework of Hadamard manifolds.

Suggested Citation

  • Balendu Bhooshan Upadhyay & Arnav Ghosh & Savin Treanţă & Jen-Chih Yao, 2024. "Constraint Qualifications and Optimality Conditions for Multiobjective Mathematical Programming Problems with Vanishing Constraints on Hadamard Manifolds," Mathematics, MDPI, vol. 12(19), pages 1-24, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3047-:d:1488312
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    References listed on IDEAS

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    1. Le Thanh Tung, 2022. "Karush–Kuhn–Tucker optimality conditions and duality for multiobjective semi-infinite programming with vanishing constraints," Annals of Operations Research, Springer, vol. 311(2), pages 1307-1334, April.
    2. S. K. Mishra & Vinay Singh & Vivek Laha, 2016. "On duality for mathematical programs with vanishing constraints," Annals of Operations Research, Springer, vol. 243(1), pages 249-272, August.
    3. Tadeusz Antczak, 2023. "On directionally differentiable multiobjective programming problems with vanishing constraints," Annals of Operations Research, Springer, vol. 328(2), pages 1181-1212, September.
    4. 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.
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