Journal of Global Optimization

, Volume 28, Issue 2, pp 175–195

Neurodynamical Optimization

  • Li-Zhi Liao
  • Houduo Qi
  • Liqun Qi
Article

DOI: 10.1023/B:JOGO.0000015310.27011.02

Cite this article as:
Liao, LZ., Qi, H. & Qi, L. Journal of Global Optimization (2004) 28: 175. doi:10.1023/B:JOGO.0000015310.27011.02

Abstract

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.

Dynamical systemNeural networkNeurodynamicalOde SystemOptimization

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Li-Zhi Liao
    • 1
  • Houduo Qi
    • 2
  • Liqun Qi
    • 2
  1. 1.Department of MathematicsHong Kong Baptist UniversityKowloon Tong, KowloonHong Kong; E-mail
  2. 2.Department of Applied MathematicsThe Hong Kong Polytechnic University, Hung HomKowloonHong Kong; E-mail