The variational gradient method

Luchka, A. Yu.; Noshchenko, O. E.; Tukalevskaya, N. I.

doi:10.1016/0041-5553(84)90222-2

Cited by 3 publications

(2 citation statements)

References 1 publication

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“…From the estimates (25), (26) it is clear that the variation-gradient method converges better than gradient-type methods. In the case B = K = I and the operator A is bounded, positive-definite, symmetric then the method (10)- (17) degenerates into an ordinary variation gradient method for a positive-definite, bounded, and symmetric operator [15].…”

Section: Variational Gradient Methods For the Investigation Of Integromentioning

confidence: 99%

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Improvement of variational-gradient method in dynamical systems of automated control for integro-differential models

Mashkov¹,

Sobchuk²,

Барабаш³

et al. 2019

Math. Model. Comput.

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The dynamical systems given by integro-differentiation models with K-symmetric K-positive-definite operator are considered. The variational-gradient method was applied to those models. The analysis showed that the implementation of this method does not require knowledge of the operator spectrum, in addition, it has a better convergence rate and is more resistant to disturbances than gradient methods. The theorem is proved in this paper, which allows us to draw conclusions about the effectiveness of the application of the variational-gradient method for the research of control problems. Investigation of an integro-differential model with a K-positive-definite K-symmetric operator using the variational-gradient method will increase the efficiency of information processing in the processes of control and research of dynamic systems. Application of the variationalgradient method to the control tasks will allow expanding the range of tasks under consideration. It is noted that the development of modern technologies entails an increase in the complexity of control objects, an increase in the quality requirements and the accuracy of control due to the increase in the cost of control error. This makes to be essential further development and improvement of methods that solve the problems of optimal control, for example, unmanned aerial vehicles. As the model example, the application of the variational-gradient method to the models of automated control systems for unmanned aerial vehicles is considered.

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Section: Variational Gradient Methods For the Investigation Of Integromentioning

confidence: 99%

“…This allows you to reduce the estimated costs, which in turn saves time and memory to implement the model in practice. Such methods include the variational-gradient method [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Improvement of variational-gradient method in dynamical systems of automated control for integro-differential models

Mashkov¹,

Sobchuk²,

Барабаш³

et al. 2019

Math. Model. Comput.

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A Modified Variational-Gradient Method for Quasilinear Equations

Luchka

2003

Cybernetics and Systems Analysis

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Minimizing of the quadratic functional on Hopfield networks

Boichuk

Bihun

Feruk

et al. 2021

Electron. J. Qual. Theory Differ. Equ.

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In this paper, we consider the continuous Hopfield model with a weak interaction of network neurons. This model is described by a system of differential equations with linear boundary conditions. Also, we consider the questions of finding necessary and sufficient conditions of solvability and constructive construction of solutions of the given problem, which turn into solutions of the linear generating problem, as the parameter $\varepsilon$ tends to zero. An iterative algorithm for finding solutions has been constructed. The problem of finding the extremum of the target functions on the given problem solution is considered. To minimize a functional, an accelerated method of conjugate gradients is used. Results are illustrated with examples for the case of three neurons.

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The variational gradient method

Cited by 3 publications

References 1 publication

Improvement of variational-gradient method in dynamical systems of automated control for integro-differential models

Improvement of variational-gradient method in dynamical systems of automated control for integro-differential models

A Modified Variational-Gradient Method for Quasilinear Equations

Minimizing of the quadratic functional on Hopfield networks

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