TY - JOUR
T1 - Global exponential stability of recurrent neural networks for solving optimization and related problems
AU - Xia, Youshen
AU - Wang, Jun
PY - 2000/7
Y1 - 2000/7
N2 - Global exponential stability is a desirable property for dynamic systems. This paper studies the global exponential stability of several existing recurrent neural networks for solving linear programming problems, convex programming problems with interval constraints, convex programming problems with nonlinear constraints, and monotone variational inequalities. In contrast to the existing results on global exponential stability, the present results do not require additional conditions on the weight matrices of recurrent neural networks and improve some existing conditions for global exponential stability. Therefore, the stability results in this paper further demonstrate the superior convergence properties of the existing neural networks for optimization.
AB - Global exponential stability is a desirable property for dynamic systems. This paper studies the global exponential stability of several existing recurrent neural networks for solving linear programming problems, convex programming problems with interval constraints, convex programming problems with nonlinear constraints, and monotone variational inequalities. In contrast to the existing results on global exponential stability, the present results do not require additional conditions on the weight matrices of recurrent neural networks and improve some existing conditions for global exponential stability. Therefore, the stability results in this paper further demonstrate the superior convergence properties of the existing neural networks for optimization.
UR - http://www.scopus.com/inward/record.url?scp=0034227388&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0034227388&origin=recordpage
U2 - 10.1109/72.857782
DO - 10.1109/72.857782
M3 - RGC 22 - Publication in policy or professional journal
SN - 1045-9227
VL - 11
SP - 1017
EP - 1022
JO - IEEE Transactions on Neural Networks
JF - IEEE Transactions on Neural Networks
IS - 4
ER -