Application of Gradient Optimization Methods in Defining Neural Dynamics
Predrag S. Stanimirović,
Nataša Tešić,
Dimitrios Gerontitis,
Gradimir V. Milovanović,
Milena J. Petrović,
Vladimir L. Kazakovtsev,
Vladislav Stasiuk
Affiliations
Predrag S. Stanimirović
Faculty of Sciences and Mathematics, University of Niš, 18000 Niš, Serbia
Nataša Tešić
Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, 21000 Novi Sad, Serbia
Dimitrios Gerontitis
Department of Information and Electronic Engineering, International Hellenic University, 57400 Thessaloniki, Greece
Gradimir V. Milovanović
Mathematical Institute, Serbian Academy of Sciences and Arts, Kneza Mihaila 35, 11000 Belgrade, Serbia
Milena J. Petrović
Faculty of Sciences and Mathematics, University of Pristina in Kosovska Mitrovica, Lole Ribara 29, 38220 Kosovska Mitrovica, Serbia
Vladimir L. Kazakovtsev
Laboratory “Hybrid Methods of Modelling and Optimization in Complex Systems”, Siberian Federal University, Prosp. Svobodny 79, 660041 Krasnoyarsk, Russia
Vladislav Stasiuk
Laboratory “Hybrid Methods of Modelling and Optimization in Complex Systems”, Siberian Federal University, Prosp. Svobodny 79, 660041 Krasnoyarsk, Russia
Applications of gradient method for nonlinear optimization in development of Gradient Neural Network (GNN) and Zhang Neural Network (ZNN) are investigated. Particularly, the solution of the matrix equation AXB=D which changes over time is studied using the novel GNN model, termed as GGNN(A,B,D). The GGNN model is developed applying GNN dynamics on the gradient of the error matrix used in the development of the GNN model. The convergence analysis shows that the neural state matrix of the GGNN(A,B,D) design converges asymptotically to the solution of the matrix equation AXB=D, for any initial state matrix. It is also shown that the convergence result is the least square solution which is defined depending on the selected initial matrix. A hybridization of GGNN with analogous modification GZNN of the ZNN dynamics is considered. The Simulink implementation of presented GGNN models is carried out on the set of real matrices.
