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A One-Layer Recurrent Neural Network with a Discontinuous Activation Function for Linear Programming

qsliu{at}mae.cuhk.edu.hk Department of Mechanical and Automation Engineering, Chinese University of Hong Kong, Shatin, New Territories, Hong Kong

Jun Wang

jwang{at}mae.cuhk.edu.hk Department of Mechanical and Automation Engineering, Chinese University of Hong Kong, Shatin, New Territories, Hong Kong

A one-layer recurrent neural network with a discontinuous activation function is proposed for linear programming. The number of neurons in the neural network is equal to that of decision variables in the linear programming problem. It is proven that the neural network with a sufficiently high gain is globally convergent to the optimal solution. Its application to linear assignment is discussed to demonstrate the utility of the neural network. Several simulation examples are given to show the effectiveness and characteristics of the neural network.