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Recurrent Neural Network Models Based on Optimization Methods

Author

Listed:
  • Predrag S. Stanimirović

    (Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia
    Laboratory “Hybrid Methods of Modelling and Optimization in Complex Systems”, Siberian Federal University, Krasnoyarsk 660041, Russia)

  • Spyridon D. Mourtas

    (Laboratory “Hybrid Methods of Modelling and Optimization in Complex Systems”, Siberian Federal University, Krasnoyarsk 660041, Russia
    Department of Economics, Division of Mathematics and Informatics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559 Athens, Greece)

  • Vasilios N. Katsikis

    (Department of Economics, Division of Mathematics and Informatics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559 Athens, Greece)

  • Lev A. Kazakovtsev

    (Laboratory “Hybrid Methods of Modelling and Optimization in Complex Systems”, Siberian Federal University, Krasnoyarsk 660041, Russia)

  • Vladimir N. Krutikov

    (Department of Applied Mathematics, Kemerovo State University, Krasnaya Street 6, Kemerovo 650043, Russia)

Abstract

Many researchers have addressed problems involving time-varying (TV) general linear matrix equations (GLMEs) because of their importance in science and engineering. This research discusses and solves the topic of solving TV GLME using the zeroing neural network (ZNN) design. Five new ZNN models based on novel error functions arising from gradient-descent and Newton optimization methods are presented and compared to each other and to the standard ZNN design. Pseudoinversion is involved in four proposed ZNN models, while three of them are related to Newton’s optimization method. Heterogeneous numerical examples show that all models successfully solve TV GLMEs, although their effectiveness varies and depends on the input matrix.

Suggested Citation

  • Predrag S. Stanimirović & Spyridon D. Mourtas & Vasilios N. Katsikis & Lev A. Kazakovtsev & Vladimir N. Krutikov, 2022. "Recurrent Neural Network Models Based on Optimization Methods," Mathematics, MDPI, vol. 10(22), pages 1-26, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4292-:d:974619
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    References listed on IDEAS

    as
    1. Simos, Theodore E. & Katsikis, Vasilios N. & Mourtas, Spyridon D., 2022. "Multi-input bio-inspired weights and structure determination neuronet with applications in European Central Bank publications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 451-465.
    2. Stanimirović, Predrag S. & Katsikis, Vasilios N. & Jin, Long & Mosić, Dijana, 2021. "Properties and computation of continuous-time solutions to linear systems," Applied Mathematics and Computation, Elsevier, vol. 405(C).
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