Distributed continuous-time accelerated neurodynamic approaches for sparse recovery via smooth approximation to L1-minimization

Abstract

This paper develops two continuous-time distributed accelerated neurodynamic approaches for solving sparse recovery via smooth approximation to L₁-norm minimization problem. First, the L₁-norm minimization problem is converted into a distributed smooth optimization problem by utilizing multiagent consensus theory and smooth approximation. Then, a distributed primal-dual accelerated neurodynamic approach is designed by using Karush-Kuhn-Tucker (KKT) condition and Nesterov's accelerated method. Furthermore, in order to reduce the structure complexity of the presented neurodynamic approach, based on the projection matrix, we eliminate a dual variable in the KKT condition and propose a distributed accelerated neurodynamic approach with a simpler structure. It is proved that the two proposed distributed neurodynamic approaches both achieve O(1t²) convergence rate. Finally, the simulation results of sparse recovery are given to demonstrate the effectiveness of the proposed approaches.

Keywords: Distributed neurodynamic approaches; Nesterov’s accelerated method; Smooth approximation; Sparse recovery.