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Constraint Qualifications for Nonsmooth Multiobjective Programming Problems with Switching Constraints on Hadamard Manifolds

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Abstract

In this article, we investigate a class of nonsmooth multiobjective mathematical optimization problems with switching constraints (abbreviated as, (NMMPSC)) in the framework of Hadamard manifolds. Corresponding to (NMMPSC), the generalized Guignard constraint qualification (abbreviated as, (GGCQ)) is introduced in the Hadamard manifold setting. Karush–Kuhn–Tucker (abbreviated as, KKT) type necessary conditions of Pareto efficiency are derived for (NMMPSC). Subsequently, we introduce several other constraint qualifications for (NMMPSC), which turn out to be sufficient conditions for (GGCQ). We have furnished non-trivial illustrative examples to justify the significance of our results. To the best of our knowledge, constraint qualifications for (NMMPSC) have not yet been studied in the Hadamard manifold framework.

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Acknowledgements

The authors would like to thank the anonymous referees for their careful reading of the paper and constructive suggestions, which have substantially improved the paper in its present form.

Funding

The second author is supported by the Council of Scientific and Industrial Research (CSIR), New Delhi, India, through the grant number 09/1023(0044)/2021-EMR-I.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Patna, Patna, India

    Balendu Bhooshan Upadhyay & Arnav Ghosh

  2. Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran

    Nader Kanzi & Hamed Soroush

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Upadhyay, B.B., Ghosh, A., Kanzi, N. et al. Constraint Qualifications for Nonsmooth Multiobjective Programming Problems with Switching Constraints on Hadamard Manifolds. Bull. Malays. Math. Sci. Soc. 47, 103 (2024). https://doi.org/10.1007/s40840-024-01701-8

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