Minimizing of the quadratic functional on Hopfield networks.
by
Victor Feruk
(Institute of Mathematics NASU), Oleksandr Pokutnyi
(Institute of Mathematics of NASU)
→
Europe/Kiev
Description
We consider the continuous Hopfield model with a weak interaction of network
neurons described by a system of differential equations with linear boundary
conditions, and discuss the questions of finding necessary and sufficient conditions
of solvability and construction of solutions of the given problem, turning into
solutions of the linear generating problem, as the parameter 𝜀 tends to zero. We
further construct an iterative algorithm for finding solutions with a quadratic rate of
convergence and consider the problem of finding the extremum of the target
functions on the problem’s solutions. The results are illustrated with examples for
the case of three neurons.
