A second-order accelerated neurodynamic approach for distributed convex optimization. (February 2022)

• Record Type: Journal Article
• Authors: Jiang, Xinrui; Qin, Sitian; Xue, Xiaoping; Liu, Xinzhi
• Is Part Of: Neural networks. Volume 146(2022)
• Page Start: 161
• Page End: 173
• Publication Date: 2022-02
• Subjects: Second-order neurodynamic approach -- Inertial systems -- Convergence rate; 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.2021.11.013
• Languages: English
• ISSNs: 0893-6080

Abstract

Abstract: Based on the theories of inertial systems, a second-order accelerated neurodynamic approach is designed to solve a distributed convex optimization with inequality and set constraints. Most of the existing approaches for distributed convex optimization problems are usually first-order ones, and it is usually hard to analyze the convergence rate for the state solution of those first-order approaches. Due to the control design for the acceleration, the second-order neurodynamic approaches can often achieve faster convergence rate. Moreover, the existing second-order approaches are mostly designed to solve unconstrained distributed convex optimization problems, and are not suitable for solving constrained distributed convex optimization problems. It is acquired that the state solution of the designed neurodynamic approach in this paper converges to the optimal solution of the considered distributed convex optimization problem. An error function which demonstrates the performance of the designed neurodynamic approach, has a superquadratic convergence. Several numerical examples are provided to show the effectiveness of the presented second-order accelerated neurodynamic approach.