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Linear Simultaneous Equations’ Neural Solution and Its Application to Convex Quadratic Programming with Equality‐Constraint

Author

Listed:
  • Yuhuan Chen
  • Chenfu Yi
  • Jian Zhong

Abstract

A gradient‐based neural network (GNN) is improved and presented for the linear algebraic equation solving. Then, such a GNN model is used for the online solution of the convex quadratic programming (QP) with equality‐constraints under the usage of Lagrangian function and Karush‐Kuhn‐Tucker (KKT) condition. According to the electronic architecture of such a GNN, it is known that the performance of the presented GNN could be enhanced by adopting different activation function arrays and/or design parameters. Computer simulation results substantiate that such a GNN could obtain the accurate solution of the QP problem with an effective manner.

Suggested Citation

  • Yuhuan Chen & Chenfu Yi & Jian Zhong, 2013. "Linear Simultaneous Equations’ Neural Solution and Its Application to Convex Quadratic Programming with Equality‐Constraint," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:695647
    DOI: 10.1155/2013/695647
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    References listed on IDEAS

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    1. Narin Petrot, 2010. "Some Existence Theorems for Nonconvex Variational Inequalities Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    2. Panpan Liu & Shugong Zhang & Qingchun Li, 2013. "On the Positive Definite Solutions of a Nonlinear Matrix Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    3. Panpan Liu & Shugong Zhang & Qingchun Li, 2013. "On the Positive Definite Solutions of a Nonlinear Matrix Equation," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-6, May.
    4. Xiongfei Zou & Ying Tang & Shirong Bu & Zhengxiang Luo & Shouming Zhong, 2013. "Neural‐Network‐Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    5. Xiongfei Zou & Ying Tang & Shirong Bu & Zhengxiang Luo & Shouming Zhong, 2013. "Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-13, March.
    6. Narin Petrot, 2010. "Some Existence Theorems for Nonconvex Variational Inequalities Problems," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-9, February.
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