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On Constraint Qualifications for Mathematical Programming Problems with Vanishing Constraints on Hadamard Manifolds

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  • Balendu Bhooshan Upadhyay

    (Indian Institute of Technology Patna)

  • Arnav Ghosh

    (Indian Institute of Technology Patna)

Abstract

This article is devoted to the study of mathematical programming problems with vanishing constraints on Hadamard manifolds (in short, MPVC-HM). We present the Abadie constraint qualification (in short, ACQ) and (MPVC-HM)-tailored ACQ for MPVC-HM and provide some necessary conditions for the satisfaction of ACQ for MPVC-HM. Moreover, we demonstrate that the Guignard constraint qualification (in short, GCQ) is satisfied for MPVC-HM under certain mild restrictions. We introduce several (MPVC-HM)-tailored constraint qualifications in the framework of Hadamard manifolds that ensure satisfaction of GCQ. Moreover, we refine our analysis and present some modified sufficient conditions which guarantee that GCQ is satisfied. Several non-trivial examples are incorporated to illustrate the significance of the derived results. To the best of our knowledge, constraint qualifications for mathematical programming problems with vanishing constraints in manifold setting have not been explored before.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:199:y:2023:i:1:d:10.1007_s10957-023-02207-2
    DOI: 10.1007/s10957-023-02207-2
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    References listed on IDEAS

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    1. Lei Guo & Gui-Hua Lin, 2013. "Notes on Some Constraint Qualifications for Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 600-616, March.
    2. Qingjie Hu & Jiguang Wang & Yu Chen, 2020. "New dualities for mathematical programs with vanishing constraints," Annals of Operations Research, Springer, vol. 287(1), pages 233-255, April.
    3. Glaydston C. Bento & Jefferson G. Melo, 2012. "Subgradient Method for Convex Feasibility on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 773-785, March.
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    6. Ali Sadeghieh & Nader Kanzi & Giuseppe Caristi & David Barilla, 2022. "On stationarity for nonsmooth multiobjective problems with vanishing constraints," Journal of Global Optimization, Springer, vol. 82(4), pages 929-949, April.
    7. Mohammad Mahdi Karkhaneei & Nezam Mahdavi-Amiri, 2019. "Nonconvex Weak Sharp Minima on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 85-104, October.
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    9. 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.
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    Cited by:

    1. 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.
    2. Harry Oviedo, 2023. "Proximal Point Algorithm with Euclidean Distance on the Stiefel Manifold," Mathematics, MDPI, vol. 11(11), pages 1-17, May.

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