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Duality for Nonsmooth Optimization Problems with Equilibrium Constraints, Using Convexificators

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  • Yogendra Pandey

    (Banaras Hindu University)

  • Shashi Kant Mishra

    (Banaras Hindu University)

Abstract

In this paper, we consider optimization problems with equilibrium constraints. We study the Wolfe-type dual problem for the optimization problems with equilibrium constraints under the convexity assumptions using convexificators. A Mond–Weir-type dual problem is also formulated and studied for the optimization problems with equilibrium constraints under convexity and generalized convexity assumptions using convexificators. Weak duality theorems are established to relate the optimization problems with equilibrium constraints and two dual programs in the framework of convexificators. Further, strong duality theorems are obtained under generalized standard Abadie constraint qualification.

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  • Yogendra Pandey & Shashi Kant Mishra, 2016. "Duality for Nonsmooth Optimization Problems with Equilibrium Constraints, Using Convexificators," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 694-707, November.
    • Handle: RePEc:spr:joptap:v:171:y:2016:i:2:d:10.1007_s10957-016-0885-2
    DOI: 10.1007/s10957-016-0885-2
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    References listed on IDEAS

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    8. Jane J. Ye & Jin Zhang, 2014. "Enhanced Karush–Kuhn–Tucker Conditions for Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 777-794, December.
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    Cited by:

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    3. Tran Van Su, 2023. "Optimality and duality for nonsmooth mathematical programming problems with equilibrium constraints," Journal of Global Optimization, Springer, vol. 85(3), pages 663-685, March.
    4. Tran Su & Dinh Dieu Hang, 2022. "Optimality and duality in nonsmooth multiobjective fractional programming problem with constraints," 4OR, Springer, vol. 20(1), pages 105-137, March.
    5. 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.
    6. Yogendra Pandey & S. K. Mishra, 2018. "Optimality conditions and duality for semi-infinite mathematical programming problems with equilibrium constraints, using convexificators," Annals of Operations Research, Springer, vol. 269(1), pages 549-564, October.
    7. Shashi Kant Mishra & Vivek Laha & Mohd Hassan, 2024. "On Quasiconvex Multiobjective Optimization and Variational Inequalities Using Greenberg–Pierskalla Based Generalized Subdifferentials," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 1169-1186, September.
    8. Bhuwan Chandra Joshi, 2021. "Some Results on Mathematical Programs with Equilibrium Constraints," SN Operations Research Forum, Springer, vol. 2(4), pages 1-18, December.

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