A complex-valued neural dynamical optimization approach and its stability analysis. (January 2015)

• Record Type: Journal Article
• Authors: Zhang, Songchuan; Xia, Youshen; Zheng, Weixing
• Is Part Of: Neural networks. Volume 61(2015:Jan.)
• Page Start: 59
• Page End: 67
• Publication Date: 2015-01
• Subjects: Complex-valued neural dynamical system -- CR Calculus -- Nonlinear convex programming -- Complex variables -- Global stability analysis; Neural computers -- Periodicals; Neural networks (Computer science) -- Periodicals; Neural networks (Neurobiology) -- Periodicals; Nervous System -- Periodicals; Ordinateurs neuronaux -- Périodiques; Réseaux neuronaux (Informatique) -- Périodiques; Réseaux neuronaux (Neurobiologie) -- Périodiques; Neural computers; Neural networks (Computer science); Neural networks (Neurobiology); Periodicals; 006.32
• DOI: 10.1016/j.neunet.2014.10.003
• Languages: English
• ISSNs: 0893-6080

Abstract

Abstract: In this paper, we propose a complex-valued neural dynamical method for solving a complex-valued nonlinear convex programming problem. Theoretically, we prove that the proposed complex-valued neural dynamical approach is globally stable and convergent to the optimal solution. The proposed neural dynamical approach significantly generalizes the real-valued nonlinear Lagrange network completely in the complex domain. Compared with existing real-valued neural networks and numerical optimization methods for solving complex-valued quadratic convex programming problems, the proposed complex-valued neural dynamical approach can avoid redundant computation in a double real-valued space and thus has a low model complexity and storage capacity. Numerical simulations are presented to show the effectiveness of the proposed complex-valued neural dynamical approach.