On modified method of multistep coordinate descent for optimal control problem for semilinear Sobolev-type model
N. A. Manakova
South Ural State University (Chelyabinsk, Russian Federation)
The paper describes a numerical method for solving the optimal control problem for a semilinear model of Sobolev-type. The method is based on both the modified projection Galerkin method and the method of multistep coordinate descent with memory. New numerical methods for solving nonlinear optimal control problems are need, because there exists a large number of applications and it is difficult to find their analytical solutions. We consider mathematical model of regulating potential distribution of speed of the filtered liquid free surface motion. In order to numerically investigate the mathematical model, we use the sufficient conditions for the existence of an optimal control by solutions of Showalter–Sidorov problem for semilinear Sobolev type equation with $s$-monotone and $p$-coercive operator. We present the results of computational experiment that demonstrate the work of the proposed numerical method.
semilinear Sobolev-type equation, optimal control problem, numerical solution, Galerkin method, method of multistep coordinate descent.
PDF file (242 kB)
MSC: 35Q93, 49J20
N. A. Manakova, “On modified method of multistep coordinate descent for optimal control problem for semilinear Sobolev-type model”, J. Comp. Eng. Math., 3:4 (2016), 59–72
Citation in format AMSBIB
\paper On modified method of multistep coordinate descent for optimal control problem for semilinear Sobolev-type model
\jour J. Comp. Eng. Math.
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