Global convergence analysis of Lagrangian networks

Many models arisen in signal and image processing can be formulated as a nonlinear convex programming problem with linear equality constraints. A Lagrangian network was developed for real-time applications of these problems. Yet, the global convergence of the Lagrangian network has not been well studied due to the asymmetry of the corresponding Lagrange system. In this brief, based on a new Lyapunov function we analyze and prove the global convergence of the Lagrangian network. Simulation examples are provided to show the effectiveness of the obtained results.