TY - JOUR
T1 - Neurodynamical optimization
AU - Liao, Li-Zhi
AU - Qi, Houduo
AU - Qi, Liqun
N1 - Funding Information:
The research of Li-Zhi Liao is supported in part by grants FRG/99-00/II-23 and FRG/00-01/II-63 of Hong Kong Baptist University. The research of Liqun Qi is supported in part by the Research Grant Council of Hong Kong.
PY - 2004/2
Y1 - 2004/2
N2 - Dynamical (or ode) system and neural network approaches for optimization have been co-existed for two decades. The main feature of the two approaches is that a continuous path starting from the initial point can be generated and eventually the path will converge to the solution. This feature is quite different from conventional optimization methods where a sequence of points, or a discrete path, is generated. Even dynamical system and neural network approaches share many common features and structures, yet a complete comparison for the two approaches has not been available. In this paper, based on a detailed study on the two approaches, a new approach, termed neurodynamical approach, is introduced. The new neurodynamical approach combines the attractive features in both dynamical (or ode) system and neural network approaches. In addition, the new approach suggests a systematic procedure and framework on how to construct a neurodynamical system for both unconstrained and constrained problems. In analyzing the stability issues of the underlying dynamical (or ode) system, the neurodynamical approach adopts a new strategy, which avoids the Lyapunov function. Under the framework of this neurodynamical approach, strong theoretical results as well as promising numerical results are obtained.
AB - Dynamical (or ode) system and neural network approaches for optimization have been co-existed for two decades. The main feature of the two approaches is that a continuous path starting from the initial point can be generated and eventually the path will converge to the solution. This feature is quite different from conventional optimization methods where a sequence of points, or a discrete path, is generated. Even dynamical system and neural network approaches share many common features and structures, yet a complete comparison for the two approaches has not been available. In this paper, based on a detailed study on the two approaches, a new approach, termed neurodynamical approach, is introduced. The new neurodynamical approach combines the attractive features in both dynamical (or ode) system and neural network approaches. In addition, the new approach suggests a systematic procedure and framework on how to construct a neurodynamical system for both unconstrained and constrained problems. In analyzing the stability issues of the underlying dynamical (or ode) system, the neurodynamical approach adopts a new strategy, which avoids the Lyapunov function. Under the framework of this neurodynamical approach, strong theoretical results as well as promising numerical results are obtained.
KW - Dynamical system
KW - Neural network
KW - Neurodynamical
KW - Ode system
KW - Optimization
UR - http://www.scopus.com/inward/record.url?scp=1542375801&partnerID=8YFLogxK
U2 - 10.1023/B:JOGO.0000015310.27011.02
DO - 10.1023/B:JOGO.0000015310.27011.02
M3 - Journal article
AN - SCOPUS:1542375801
SN - 0925-5001
VL - 28
SP - 175
EP - 195
JO - Journal of Global Optimization
JF - Journal of Global Optimization
IS - 2
ER -