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On quasidifferentiable mathematical programs with equilibrium constraints

Author

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  • Vivek Laha

    (Banaras Hindu University)

  • Harsh Narayan Singh

    (Banaras Hindu University)

Abstract

The aim of this article is to study mathematical programs with equilibrium constraints involving quasidifferentiable functions, denoted by QMPEC, and to synthesize suitable optimality conditions. We first derive Fritz-John (FJ) necessary optimality conditions with Lagrange multipliers depending upon the choice of superdifferentials. We introduce a suitable variant of no nonzero abnormal multiplier constraint qualification for the QMPEC, denoted by NNAMCQ-QMPEC, and derive Karush–Kuhn–Tucker (KKT) necessary optimality conditions. We also propose some conditions under which the Lagrange multipliers do not depend upon the choice of superdifferentials. Further, we prove several sufficient optimality conditions for a weak stationary point to be optimal for the QMPEC under suitable choice of generalized convex functions.

Suggested Citation

  • Vivek Laha & Harsh Narayan Singh, 2023. "On quasidifferentiable mathematical programs with equilibrium constraints," Computational Management Science, Springer, vol. 20(1), pages 1-20, December.
    • Handle: RePEc:spr:comgts:v:20:y:2023:i:1:d:10.1007_s10287-023-00461-3
    DOI: 10.1007/s10287-023-00461-3
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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.
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    3. T. Antczak, 2016. "Optimality Conditions in Quasidifferentiable Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 708-725, November.
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    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.
    7. Majid E. Abbasov, 2017. "Comparison Between Quasidifferentials and Exhausters," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 59-75, October.
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