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Constraint Qualifications and Optimality Criteria for Nonsmooth Multiobjective Programming Problems on Hadamard Manifolds

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Abstract

This article deals with a class of constrained nonsmooth multiobjective programming problems (NMOPP) in the setting of Hadamard manifolds. The generalized Guignard constraint qualification (GGCQ), Abadie constraint qualification (ACQ), and the generalized ACQ (GACQ) are introduced in the framework of Hadamard manifolds for NMOPP using the notion of Clarke subdifferentials. Subsequently, by employing GGCQ and geodesic quasiconvexity assumptions, we establish Karush–Kuhn–Tucker (abbreviated as, KKT)-type necessary criteria of Pareto efficiency for NMOPP. Moreover, we establish that ACQ and GACQ are sufficient criteria for satisfaction of GGCQ. Several nontrivial numerical examples are furnished in manifold settings to demonstrate the validity of the derived results. To the best of our knowledge, this is the first time that ACQ, GACQ, GGCQ, and KKT-type necessary criteria of Pareto efficiency for NMOPP have been studied in manifold setting using Clarke subdifferentials.

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Acknowledgements

The authors would like to thank the anonymous referees for their careful reading of the manuscript and constructive suggestions, which have substantially improved the paper in its present form. The second author is supported by the Council of Scientific and Industrial Research (CSIR), New Delhi, India, through 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 Applied Mathematics, University Politehnica of Bucharest, 060042, Bucharest, Romania

    Savin Treanţă

  3. Academy of Romanian Scientists, 54 Splaiul Independentei, 050094, Bucharest, Romania

    Savin Treanţă

  4. Fundamental Sciences Applied in Engineering Research Center (SFAI), University Politehnica of Bucharest, 060042, Bucharest, Romania

    Savin Treanţă

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  1. Balendu Bhooshan Upadhyay
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Upadhyay, B.B., Ghosh, A. & Treanţă, S. Constraint Qualifications and Optimality Criteria for Nonsmooth Multiobjective Programming Problems on Hadamard Manifolds. J Optim Theory Appl 200, 794–819 (2024). https://doi.org/10.1007/s10957-023-02301-5

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