A One-Layer Recurrent Neural Network for Non-smooth Convex Optimization Subject to Linear Equality Constraints

In this paper, a one-layer recurrent neural network is proposed for solving non-smooth convex optimization problems with linear equality constraints. Comparing with the existing neural networks, the proposed neural network has simpler architecture and the number of neurons is the same as that of decision variables in the optimization problems. The global convergence of the neural network can be guaranteed if the non-smooth objective function is convex. Simulation results are provided to show that the state trajectories of the neural network can converge to the optimal solutions of the non-smooth convex optimization problems and show the performance of the proposed neural network.