Control and Optimization in Applied Mathematics

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A KKT-Based Neurodynamic Framework for CCR-DEA: Lyapunov Stability Analysis and Application to Asian Games Efficiency Evaluation

Articles in Press

Document Type : Research Article

Authors

1 Department of Applied Mathematics, Faculty of Basic Sciences, Shahid Sattari University of Aeronautical Science and Technology, Tehran, Iran

2 Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran

3 Department of Sport Management and Motor Behavior, Faculty of Sport Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

4 Mathematical Biology Research Laboratory (MBRL), Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

Abstract

 Data envelopment analysis (DEA) is a widely used non-parametric method for evaluating the relative efficiency of peer decision-making units (DMUs). To address the computational demands of conventional solvers, this study develops a neurodynamic optimization framework derived from the Karush--Kuhn--Tucker (KKT) optimality conditions of the CCR-based, input-oriented DEA model. To date, only a few studies have applied neurodynamic approaches to DEA, and all of them rely on double-layer structures. Our primary contribution is the construction of a KKT-based dynamic system tailored to the CCR-based DEA formulation. Furthermore, we provide a rigorous theoretical foundation by establishing the Lyapunov stability of the proposed system, thereby ensuring its global convergence to an exact optimal solution. The model's practical effectiveness is validated through a comprehensive case study analyzing the efficiency of participating nations in the Asian Games. The results, obtained using our neurodynamic framework and evaluated in terms of CPU time, demonstrate its robustness and computational efficiency for real-world performance benchmarking.

Highlights

  • A KKT-based single-layer neurodynamic model is proposed for CCR-DEA problems.
  • The model is derived directly from the KKT conditions of the CCR-DEA LP.
  • Lyapunov stability and global convergence of the model are rigorously proven.
  • The model is applied to evaluate Iran's efficiency across 14 Asian Games.
  • The proposed model achieves lower CPU time than three benchmark neurodynamic models.

Keywords

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References
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Control and Optimization in Applied Mathematics

Articles in Press, Accepted Manuscript
Available Online from 14 July 2026
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