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An Exact Schur Complement Method for Time-Harmonic Optimal Control Problems

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Abstract

By use of Fourier time series expansions in an angular frequency variable, time-harmonic optimal control problems constrained by a linear differential equation decouples for the different frequencies. Hence, for the analysis of a solution method one can consider the frequency as a parameter. There are three variables to be determined, the state solution, the control variable, and the adjoint variable.

The first order optimality conditions lead to a three-by-three block matrix system where the adjoint optimality variable can be eliminated. For the so arising two-by-two block system, in this paper we study a factorization method involving an exact Schur complement method and illustrate the performance of an inexact version of it.

Supported by EU Horizon 2020 research and innovation programme, grant agreement number 847593; the Czech Radioactive Waste Repository Authority (SÚRAO), grant agreement number SO2020-017; VR Grant 2017-03749 Mathematics and numerics in PDE-constrained optimization problems with state and control constraints, 2018-2022.

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Authors and Affiliations

  1. The Czech Academy of Sciences, Institute of Geonics, Ostrava, Czech Republic

    Owe Axelsson, Dalibor Lukáš & Maya Neytcheva

  2. Department of Information Technology, Uppsala University, Uppsala, Sweden

    Owe Axelsson, Dalibor Lukáš & Maya Neytcheva

  3. VSB - University of Technology, Ostrava, Czech Republic

    Owe Axelsson, Dalibor Lukáš & Maya Neytcheva

Authors
  1. Owe Axelsson
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  2. Dalibor Lukáš
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  3. Maya Neytcheva
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Corresponding author

Correspondence to Maya Neytcheva .

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Editors and Affiliations

  1. IICT-BAS, Sofia, Bulgaria

    Ivan Lirkov

  2. IICT-BAS, Sofia, Bulgaria

    Svetozar Margenov

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Axelsson, O., Lukáš, D., Neytcheva, M. (2022). An Exact Schur Complement Method for Time-Harmonic Optimal Control Problems. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2021. Lecture Notes in Computer Science, vol 13127. Springer, Cham. https://doi.org/10.1007/978-3-030-97549-4_10

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  • DOI: https://doi.org/10.1007/978-3-030-97549-4_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-97548-7

  • Online ISBN: 978-3-030-97549-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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