TY - GEN

T1 - Convergence of a recurrent neural network for nonconvex optimization based on an augmented lagrangian function

AU - Hu, Xiaolin

AU - Wang, Jun

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=38049150429&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-72395-0_25

DO - 10.1007/978-3-540-72395-0_25

M3 - Conference contribution

AN - SCOPUS:38049150429

SN - 9783540723943

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 194

EP - 203

BT - Advances in Neural Networks - ISNN 2007 - 4th International Symposium on Neural Networks, ISNN 2007, Proceedings

PB - Springer Verlag

T2 - 4th International Symposium on Neural Networks, ISNN 2007

Y2 - 3 June 2007 through 7 June 2007

ER -