Convergence of a Recurrent Neural Network for Nonconvex Optimization Based on an Augmented Lagrangian Function

In the paper, a recurrent neural network based on an augmented Lagrangian function is proposed for seeking local minima of nonconvex optimization problems with inequality constraints. First, each equilibrium point of the neural network corresponds to a Karush-KuhnTucker (KKT) point of the problem. Second, by appropriately choosing a control parameter, the neural network is asymptotically stable at those local minima satisfying some mild conditions. The latter property of the neural network is ensured by the convexification capability of the augmented Lagrangian function. The proposed scheme is inspired by many existing neural networks in the literature and can be regarded as an extension or improved version of them. A simulation example is discussed to illustrate the results.