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On stationarity for nonsmooth multiobjective problems with vanishing constraints

Author

Listed:
  • Ali Sadeghieh

    (Islamic Azad University)

  • Nader Kanzi

    (Payame Noor University)

  • Giuseppe Caristi

    (University of Messina)

  • David Barilla

    (University of Messina)

Abstract

The aim of this paper is to develop first-order necessary and sufficient optimality conditions for nonsmooth multiobjective optimization problems with vanishing constraints. First of all, we introduce some data qualifications for the problem, and derive the comparisons between them. Secondly, based on the mentioned qualifications, we demonstrate some necessary optimality conditions, named strongly stationary conditions, at weakly efficient and efficient solutions of considered problem. Then, we show that the strongly stationary conditions are also sufficient for optimality. Finally, using the tightened problems, we establish other classes of qualifications and stationary conditions.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:82:y:2022:i:4:d:10.1007_s10898-021-01030-1
    DOI: 10.1007/s10898-021-01030-1
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    References listed on IDEAS

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    1. S. K. Mishra & B. B. Upadhyay & Le Thi Hoai An, 2014. "Lagrange Multiplier Characterizations of Solution Sets of Constrained Nonsmooth Pseudolinear Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 763-777, March.
    2. HALKIN, Hubert, 1974. "Implicit functions and optimization problems without continuous differentiability of the data," LIDAM Reprints CORE 184, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Nooshin Movahedian, 2017. "Bounded Lagrange multiplier rules for general nonsmooth problems and application to mathematical programs with equilibrium constraints," Journal of Global Optimization, Springer, vol. 67(4), pages 829-850, April.
    4. Sajjad Kazemi & Nader Kanzi, 2018. "Constraint Qualifications and Stationary Conditions for Mathematical Programming with Non-differentiable Vanishing Constraints," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 800-819, December.
    5. X. F. Li, 2000. "Constraint Qualifications in Nonsmooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 373-398, August.
    6. 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.
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    Cited by:

    1. Hui Huang & Haole Zhu, 2022. "Stationary Condition for Borwein Proper Efficient Solutions of Nonsmooth Multiobjective Problems with Vanishing Constraints," Mathematics, MDPI, vol. 10(23), pages 1-18, December.
    2. 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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