Neurodynamical optimization

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.