Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/31646
Title: Stability analysis of gradient-based neural networks for optimization problems
Authors: Han, Q
Liao, LZ
Qi, H
Qi, L 
Keywords: Asymptotic stability
Equilibrium point
Equilibrium set
Exponential stability
Gradient-based neural network
Issue Date: 2001
Publisher: Kluwer Academic Publ
Source: Journal of global optimization, 2001, v. 19, no. 4, p. 363-381 How to cite?
Journal: Journal of global optimization 
Abstract: The paper introduces a new approach to analyze the stability of neural network models without using any Lyapunov function. With the new approach, we investigate the stability properties of the general gradient-based neural network model for optimization problems. Our discussion includes both isolated equilibrium points and connected equilibrium sets which could be unbounded. For a general optimization problem, if the objective function is bounded below and its gradient is Lipschitz continuous, we prove that (a) any trajectory of the gradient-based neural network converges to an equilibrium point, and (b) the Lyapunov stability is equivalent to the asymptotical stability in the gradient-based neural networks. For a convex optimization problem, under the same assumptions, we show that any trajectory of gradient-based neural networks will converge to an asymptotically stable equilibrium point of the neural networks. For a general nonlinear objective function, we propose a refined gradient-based neural network, whose trajectory with any arbitrary initial point will converge to an equilibrium point, which satisfies the second order necessary optimality conditions for optimization problems. Promising simulation results of a refined gradient-based neural network on some problems are also reported.
URI: http://hdl.handle.net/10397/31646
ISSN: 0925-5001
EISSN: 1573-2916
DOI: 10.1023/A:1011245911067
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