Optimization by means of neural networks for combinatorial problems. On the Uesaka's conjecture

This paper shows the possibility that, as the Uesaka's conjecture states, the globally optimum solution (not a local minimum solution) of a kind of combinatorial problem represented by a quadratic function may be obtained by solving a differential equation. For this purpose we consider a class...

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Bibliographic Details
Published in1997 IEEE International Symposium on Circuits and Systems Vol. 1; pp. 617 - 620 vol.1
Main Authors Nishi, T., Imai, K.
Format Conference Proceeding
LanguageEnglish
Japanese
Published IEEE 22.11.2002
Subjects
Computer science
Convergence
Differential equations
Hopfield neural networks
Neural networks
Traveling salesman problems
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ISBN9780780335837
078033583X
DOI10.1109/ISCAS.1997.608881

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Summary:This paper shows the possibility that, as the Uesaka's conjecture states, the globally optimum solution (not a local minimum solution) of a kind of combinatorial problem represented by a quadratic function may be obtained by solving a differential equation. For this purpose we consider a class of objective functions, f(x)=H/sup t/DHx, where H is an Hadamard matrix and D a diagonal matrix. Furthermore, we extend the above class of functions to more general class of functions. Thus the result seems to support that the Uesaka's conjecture may hold true.
ISBN:9780780335837
078033583X
DOI:10.1109/ISCAS.1997.608881