Open AccessMinimizing of the quadratic functional on Hopfield networks
Author(s) -
О. A. Boichuk,
D. S. Bihun,
V. A. Feruk,
O. O. Pokutnyi
Publication year - 2021
Publication title -
electronic journal on the qualitative theory of differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.524
H-Index - 33
ISSN - 1417-3875
DOI - 10.14232/ejqtde.2021.1.92
Subject(s) - mathematics , constructive , hopfield network , quadratic equation , mathematical optimization , boundary (topology) , boundary value problem , artificial neural network , mathematical analysis , computer science , artificial intelligence , geometry , process (computing) , operating system
In this paper, we consider the continuous Hopfield model with a weakinteraction of network neurons. This model is described by a system ofdifferential equations with linear boundary conditions. Also, we considerthe questions of finding necessary and sufficient conditions of solvabilityand constructive construction of solutions of the given problem, which turninto solutions of the linear generating problem, as the parameter$\varepsilon$ tends to zero. An iterative algorithm for finding solutionshas been constructed. The problem of finding the extremum of the targetfunctions on the given problem solution is considered. To minimize afunctional, an accelerated method of conjugate gradients is used. Resultsare illustrated with examples for the case of three neurons.