一种求解二阶锥互补问题的神经网络方法
A Neural Network Approach for Solving Second-Order Cone Complementarity Problem
摘要: 本文提出了一种用于求解二阶锥互补问题(SOCCP)的Hopfield型神经动力学框架。通过引入单参数族的平滑价值函数，将SOCCP重构为无约束优化问题，并采用微分方程进行求解。理论分析表明，该方法能保证在适当条件下实现指数稳定性。同时数值实验验证了该方法的可行性，MATLAB仿真结果表明，该神经网络模型具有优异的稳定性和适应性。
Abstract: This paper introduces a Hopfield-type neural dynamic framework designed to address the second-order cone complementarity problem (SOCCP). By introducing a single-parametric class of smooth merit functions, the SOCCP is reformulated as an unconstrained optimization problem and solved via differential equations. Theoretical results confirm that the proposed approach guarantees exponential stability under appropriate conditions. Numerical experiments validate the feasibility of the method, demonstrating that, the neural network model exhibits super stability and adaptability in MATLAB simulations.
文章引用：杨嘉妮, 张杰, 邓雯. 一种求解二阶锥互补问题的神经网络方法[J]. 动力系统与控制, 2025, 14(4): 340-345. https://doi.org/10.12677/dsc.2025.144034

参考文献

[1] Tang, J.Y., Li, D., Zhou, J.C. and Sun, L. (2014) A Smoothing-Type Algorithm for the Second-Order Cone Complementarity Problem with a New Nonmonotone Line Search. Optimization, 64, 1935-1955. [Google Scholar] [CrossRef] 
[2] Miao, X.H., Chen, J.S. and Ko, C.H. (2014) A Smoothed NR Neural Network for Solving Nonlinear Convex Programs with Second-Order Cone Constraints. Information Sciences, 268, 255-270.
[3] He, X., Huang, J.J. and Li, C.J. (2018) Neural Network with Added Inertia for Linear Complementarity Problem. 2018 15th International Conference on Control, Automation, Robotics and Vision (ICARCV), Singapore, 18-21 November 2018, 1-6. [Google Scholar] [CrossRef] 
[4] Gao, X.B. and Wang, J. (2011) A Neural Network for a Class of Horizontal Linear Complementary Problems. 2011 7th International Conference on Computational Intelligence and Security, Sanya, 3-4 December 2011, 1-5. [Google Scholar] [CrossRef] 
[5] Hou, B., Zhang, J. and Qiu, C. (2022) A Neural Network for a Generalized Vertical Complementarity Problem. AIMS Mathematics, 7, 6650-6668. [Google Scholar] [CrossRef] 
[6] Fukushima, M., Luo, Z.Q. and Tseng, P. (2002) Smoothing Functions for Second-Order-Cone Complementarity Problems. SIAM Journal on Optimization, 12, 436-460. [Google Scholar] [CrossRef] 
[7] Zhang, L., Yang, W.H., Shen, C. and Li, R. (2015) A Krylov Subspace Method for Large-Scale Second-Order Cone Linear Complementarity Problem. SIAM Journal on Scientific Computing, 37, A2046-A2075. [Google Scholar] [CrossRef] 
[8] Hao, Z.J., Wan, Z.P., Chi, X.N. and Chen, J.W. (2015) A Power Penalty Method for Second-Order Cone Nonlinear Complementarity Problems. Journal of Computational and Applied Mathematics, 290, 136-149. [Google Scholar] [CrossRef] 
[9] Zhang, X.S., Liu, S.Y. and Liu, Z.H. (2009) Analysis of a Smoothing Newton Method for Second-Order Cone Complementarity Problem. Journal of Applied Mathematics and Computing, 31, 459-473. [Google Scholar] [CrossRef] 
[10] Pan, S.H. and Chen, J.S. (2010) A Proximal Gradient Descent Method for the Extended Second-Order Cone Linear Complementarity Problem. Journal of Mathematical Analysis and Applications, 366, 164-180. [Google Scholar] [CrossRef] 
[11] Pan, S.H. and Chen, J.S. (2008) A Damped Gauss-Newton Method for the Second-Order Cone Complementarity Problem. Applied Mathematics and Optimization, 59, 293-318. [Google Scholar] [CrossRef] 
[12] De Luca, T., Facchinei, F. and Kanzow, C. (1996) A Semismooth Equation Approach to the Solution of Nonlinear Complementarity Problems. Mathematical Programming, 75, 407-439. [Google Scholar] [CrossRef] 
[13] Zabczyk, J. (2020) Mathematical Control Theory. Springer.
[14] Chen, J.S. and Pan, S.H. (2008) A One-Parametric Class of Merit Functions for the Second-Order Cone Complementarity Problem. Computational Optimization and Applications, 45, 581-606. [Google Scholar] [CrossRef] 
[15] Chi, X.N., Wan, Z.P. and Hao, Z.J. (2013) A Two-Parametric Class of Merit Functions for the Second-Order Cone Complementarity Problem. Journal of Applied Mathematics, 2013, Article ID: 571927. [Google Scholar] [CrossRef] 
[16] Pan, S.H. and Chen, J.S. (2008) A Semismooth Newton Method for SOCCPs Based on a One-Parametric Class of SOC Complementarity Functions. Computational Optimization and Applications, 45, 59-88. [Google Scholar] [CrossRef] 
[17] Liao, L.Z., Qi, H.D. and Qi, L.Q. (2001) Solving Nonlinear Complementarity Problems with Neural Networks: A Reformulation Method Approach. Journal of Computational and Applied Mathematics, 131, 343-359. [Google Scholar] [CrossRef] 
[18] Qi, L.Q. and Sun, J. (1993) A Nonsmooth Version of Newton’s Method. Mathematical Programming, 58, 353-367. [Google Scholar] [CrossRef] 

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