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On complete stability of linear and quadratic programming neural networks
Author(s) -
Forti Mauro
Publication year - 2002
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.209
Subject(s) - artificial neural network , equilibrium point , quadratic equation , stability (learning theory) , state (computer science) , class (philosophy) , mathematics , quadratic programming , computer science , point (geometry) , mathematical optimization , control theory (sociology) , algorithm , differential equation , artificial intelligence , mathematical analysis , geometry , control (management) , machine learning
The paper addresses complete stability (CS) of the important class of neural networks to solve linear and quadratic programming problems introduced by Kennedy and Chua ( IEEE Trans. Circuits Syst. , 1988; 35 : 554). By CS it is meant that each trajectory converges to a stationary state, i.e. an equilibrium point of the neural network. It is shown that the neural networks in ( IEEE Trans. Circuits Syst. , 1988; 35 : 554) enjoy the property of CS even in the most general case where there are infinite non‐isolated equilibrium points. This result, which is proved by exploiting a new method to analyse CS ( Int. J. Bifurcation Chaos 2001; 11 : 655), extends the stability analysis by Kennedy and Chua ( IEEE Trans. Circuits Syst. , 1988; 35 : 554) to situations of interest where the optimization problems have infinite solutions. Copyright © 2002 John Wiley & Sons, Ltd.