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<p>In this paper, we study a Mathematical Programming with Vanishing Constraints (MPVC) and present a neural network model that employs smoothing and regularization techniques. Owing to the existence of critical kinks in the feasible set and the nonsmooth nature of the standard Karush–Kuhn–Tucker (KKT) conditions with respect to the multipliers in (MPVC), we reformulate the (MPVC) problem as a Smooth Nonlinear Programming (SNLP(r)) problem, thereby addressing the shortcomings inherent in the original (MPVC) formulation. Subsequently, the optimal solution of the transformed nonlinear problem is approximated using a dual-based neural network model. Theoretical analysis demonstrates that the equilibrium of the network is asymptotically stable and converges to the optimal solution of the (MPVC) problem. Simulation results further support the theoretical findings and confirm the computational efficiency of the proposed model.</p>

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A dual based neural network model for mathematical programs having vanishing constraints with applications

  • 期刊论文

  • 发表日期：

    2026年2月19日

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  • Anurag Jayswal,
  • Ajeet Kumar,
  • Alireza Nazemi

摘要

In this paper, we study a Mathematical Programming with Vanishing Constraints (MPVC) and present a neural network model that employs smoothing and regularization techniques. Owing to the existence of critical kinks in the feasible set and the nonsmooth nature of the standard Karush–Kuhn–Tucker (KKT) conditions with respect to the multipliers in (MPVC), we reformulate the (MPVC) problem as a Smooth Nonlinear Programming (SNLP(r)) problem, thereby addressing the shortcomings inherent in the original (MPVC) formulation. Subsequently, the optimal solution of the transformed nonlinear problem is approximated using a dual-based neural network model. Theoretical analysis demonstrates that the equilibrium of the network is asymptotically stable and converges to the optimal solution of the (MPVC) problem. Simulation results further support the theoretical findings and confirm the computational efficiency of the proposed model.