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Analysis of time‐varying cellular neural networks for quadratic global optimization
Author(s) -
Gilli M.,
Civalleri P. P.,
Roska T.,
Chua L. O.
Publication year - 1998
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/(sici)1097-007x(199803/04)26:2<109::aid-cta994>3.0.co;2-o
Subject(s) - quadratic equation , dimension (graph theory) , cellular neural network , global optimization , artificial neural network , function (biology) , algorithm , quadratic function , mathematics , invariant (physics) , computer science , activation function , topology (electrical circuits) , mathematical optimization , combinatorics , artificial intelligence , geometry , evolutionary biology , mathematical physics , biology
The algorithm for quadratic global optimization performed by a cellular neural network (CNN) with a slowly varying slope of the output characteristic (see References 1 and 2) is analysed. It is shown that the only CNN which finds the global minimum of a quadratic function for any values of the input parameters is the network composed by only two cells. If the dimension is higher than two, even the CNN described by the simplest one‐dimensional space‐invariant template  =[ A 1 , A 0 , A 1 ], fails to find the global minimum in a subset of the parameter space. Extensive simulations show that the CNN described by the above three‐element template works correctly within several parameter ranges; however, if the parameters are chosen according to a random algorithm, the error rate increases with the number of cells. © 1998 John Wiley & Sons, Ltd.