An Augmented Lagrangian Neural Network for the Fixed-Time Solution of Linear Programming

In this paper, a recurrent neural network is proposed using the augmented Lagrangian method for solving linear programming problems. The design of this neural network is based on the Karush-Kuhn-Tucker (KKT) optimality conditions and on a function that guarantees fixed-time convergence. With this aim, the use of slack variables allows transforming the initial linear programming problem into an equivalent one which only contains equality constraints. Posteriorly, the activation functions of the neural network are designed as fixed time controllers to meet KKT optimality conditions. Simulations results in an academic example and an application example show the effectiveness of the neural network.