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Optimization Control Problems for Systems Described by Elliptic Variational Inequalities with State Constraints

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Methods of Fourier Analysis and Approximation Theory

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

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Abstract

The control system described by variational inequality is considered. It is approximated by the system described by a nonlinear equation with using the penalty method. The convergence of the approximate method is proved. The necessary conditions of optimality for approximate optimization control problem are obtained. The optimal control for the approximate optimization problem is chosen as an approximate solution of the initial problem.

Mathematics Subject Classification (2000). Primary 49K20, Secondary 35J85

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Authors and Affiliations

  1. al-Farabi Kazakh national university, 71 al Farabi avenue, 050078, Almaty, Kazakhstan

    Simon Serovajsky PhD (Professor)

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  1. Simon Serovajsky PhD
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Correspondence to Simon Serovajsky PhD .

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Editors and Affiliations

  1. Department of Mathematics, Imperial College London, London, United Kingdom

    Michael Ruzhansky

  2. ICREA Research Professor, Centre de Recerca MatemĂ tica, Barcelona, Spain

    Sergey Tikhonov

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Serovajsky, S. (2016). Optimization Control Problems for Systems Described by Elliptic Variational Inequalities with State Constraints. In: Ruzhansky, M., Tikhonov, S. (eds) Methods of Fourier Analysis and Approximation Theory. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-27466-9_14

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