Two Projection Neural Networks With Reduced Model Complexity for Nonlinear Programming

• Published in: IEEE transaction on neural networks and learning systems Vol. 31; no. 6; pp. 2020 - 2029
• Main Authors: Xia, Youshen, Wang, Jun, Guo, Wenzhong
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.06.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: 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
• DOI: 10.1109/TNNLS.2019.2927639

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.