title: A complex-valued neural dynamical optimization approach and its stability analysis.
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.
authors.affiliation: Center for Discrete Mathematics and Theoretical Computer Science, Fuzhou University, Fuzhou, China.
authors.forename: Songchuan
authors.initials: S
authors.lastname: Zhang
authors.forename: Youshen
authors.initials: Y
authors.lastname: Xia
authors.forename: Weixing
authors.initials: W
authors.lastname: Zheng
mesh_terms: D008962:Models, Theoretical; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics