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A Cooperative Recurrent Neural Network for Solving L₁ Estimation Problems with General Linear Constraints

ysxia2001{at}yahoo.com College of Mathematics and Computer Science, Fuzhou University, China

Mohamed S. Kamel

mkamel{at}pami.uwaterloo.ca Department of Electrical and Computer Engineering, University of Waterloo, Canada

The constrained L₁ estimation is an attractive alternative to both the unconstrained L₁ estimation and the least square estimation. In this letter, we propose a cooperative recurrent neural network (CRNN) for solving L₁ estimation problems with general linear constraints. The proposed CRNN model combines four individual neural network models automatically and is suitable for parallel implementation. As a special case, the proposed CRNN includes two existing neural networks for solving unconstrained and constrained L₁ estimation problems, respectively. Unlike existing neural networks, with penalty parameters, for solving the constrained L₁ estimation problem, the proposed CRNN is guaranteed to converge globally to the exact optimal solution without any additional condition. Compared with conventional numerical algorithms, the proposed CRNN has a low computational complexity and can deal with the L₁ estimation problem with degeneracy. Several applied examples show that the proposed CRNN can obtain more accurate estimates than several existing algorithms.