Two Projection Neural Networks With Reduced Model Complexity for Nonlinear Programming

Recent reports show that projection neural networks with a low-dimensional state space can enhance computation speed obviously. This paper proposes two projection neural networks with reduced model dimension and complexity (RDPNNs) for solving nonlinear programming (NP) problems. Compared with exist...

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Veröffentlicht in:IEEE transaction on neural networks and learning systems Jg. 31; H. 6; S. 2020 - 2029
Hauptverfasser: Xia, Youshen, Wang, Jun, Guo, Wenzhong
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States IEEE 01.06.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Complexity
Computation
Computational complexity
Concave programming
Convex programming
fast computation
global stability
Hessian matrices
Lagrangian function
low-dimensional state space
Mathematical analysis
Matrix methods
Neural networks
nonconvex programming
Nonlinear programming
Optimization
Projection
Quadratic programming
ISSN:2162-237X, 2162-2388, 2162-2388
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Zusammenfassung:Recent reports show that projection neural networks with a low-dimensional state space can enhance computation speed obviously. This paper proposes two projection neural networks with reduced model dimension and complexity (RDPNNs) for solving nonlinear programming (NP) problems. Compared with existing projection neural networks for solving NP, the proposed two RDPNNs have a low-dimensional state space and low model complexity. Under the condition that the Hessian matrix of the associated Lagrangian function is positive semi-definite and positive definite at each Karush-Kuhn-Tucker point, the proposed two RDPNNs are proven to be globally stable in the sense of Lyapunov and converge globally to a point satisfying the reduced optimality condition of NP. Therefore, the proposed two RDPNNs are theoretically guaranteed to solve convex NP problems and a class of nonconvex NP problems. Computed results show that the proposed two RDPNNs have a faster computation speed than the existing projection neural networks for solving NP problems.
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ISSN:2162-237X
2162-2388
2162-2388
DOI:10.1109/TNNLS.2019.2927639