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Solving mathematical programs with vanishing constraints using a gradient-based neural network model

Author

Listed:
  • Rawat, Anjali
  • Singh, Vinay
  • Nazemi, Alireza

Abstract

In this paper, a gradient-based neural network model is applied to successfully determine the solution of a class of nonlinear optimization problems known as Mathematical Programs with Vanishing Constraints (MPVC). First, a smoothing and regularization technique is used to transform the original MPVC problem into a smooth and relaxed nonlinear optimization problem. Then, by utilizing the penalty function method and a gradient-based neural network model, the optimal solution of the transformed nonlinear problem is estimated. The proposed model has a straightforward structure and low computing cost. Theoretical investigation of the neural network has shown that the equilibrium of the suggested network is asymptotically stable and converges to the optimal solution of the original MPVC. Simulation results provide additional evidence that supports the theoretical analysis and confirms the computational efficiency of the suggested network.

Suggested Citation

  • Rawat, Anjali & Singh, Vinay & Nazemi, Alireza, 2026. "Solving mathematical programs with vanishing constraints using a gradient-based neural network model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 1097-1116.
    • Handle: RePEc:eee:matcom:v:239:y:2026:i:c:p:1097-1116
    DOI: 10.1016/j.matcom.2025.07.065
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    References listed on IDEAS

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    1. Michael N. Jung & Christian Kirches & Sebastian Sager, 2013. "On Perspective Functions and Vanishing Constraints in Mixed-Integer Nonlinear Optimal Control," Springer Books, in: Michael Jünger & Gerhard Reinelt (ed.), Facets of Combinatorial Optimization, edition 127, pages 387-417, Springer.
    2. S. K. Mishra & Vinay Singh & Vivek Laha & R. N. Mohapatra, 2015. "On Constraint Qualifications for Multiobjective Optimization Problems with Vanishing Constraints," Springer Books, in: Honglei Xu & Song Wang & Soon-Yi Wu (ed.), Optimization Methods, Theory and Applications, edition 127, chapter 0, pages 95-135, Springer.
    3. Matúš Benko & Helmut Gfrerer, 2017. "An SQP method for mathematical programs with vanishing constraints with strong convergence properties," Computational Optimization and Applications, Springer, vol. 67(2), pages 361-399, June.
    4. A. Izmailov & A. Pogosyan, 2012. "Active-set Newton methods for mathematical programs with vanishing constraints," Computational Optimization and Applications, Springer, vol. 53(2), pages 425-452, October.
    5. Le Thanh Tung, 2022. "Karush–Kuhn–Tucker optimality conditions and duality for multiobjective semi-infinite programming with vanishing constraints," Annals of Operations Research, Springer, vol. 311(2), pages 1307-1334, April.
    6. Wolfgang Achtziger & Tim Hoheisel & Christian Kanzow, 2013. "A smoothing-regularization approach to mathematical programs with vanishing constraints," Computational Optimization and Applications, Springer, vol. 55(3), pages 733-767, July.
    7. 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.
    8. Tassouli, Siham & Lisser, Abdel, 2023. "A neural network approach to solve geometric programs with joint probabilistic constraints," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 765-777.
    9. Balendu Bhooshan Upadhyay & Arnav Ghosh & Savin Treanţă & Jen-Chih Yao, 2024. "Constraint Qualifications and Optimality Conditions for Multiobjective Mathematical Programming Problems with Vanishing Constraints on Hadamard Manifolds," Mathematics, MDPI, vol. 12(19), pages 1-24, September.
    10. 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.
    11. Tamanna Yadav & S. K. Gupta & Sumit Kumar, 2024. "Optimality analysis and duality conditions for a class of conic semi-infinite program having vanishing constraints," Annals of Operations Research, Springer, vol. 340(2), pages 1091-1123, September.
    12. Tadeusz Antczak, 2022. "Optimality conditions and Mond–Weir duality for a class of differentiable semi-infinite multiobjective programming problems with vanishing constraints," 4OR, Springer, vol. 20(3), pages 417-442, September.
    13. Tadeusz Antczak, 2023. "On directionally differentiable multiobjective programming problems with vanishing constraints," Annals of Operations Research, Springer, vol. 328(2), pages 1181-1212, September.
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