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Optimization of a Fractional Differential Equation

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Frontiers in PDE-Constrained Optimization

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 163))

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Abstract

We consider a linear quadratic optimization problem where the state is governed by a fractional ordinary differential equation. We also consider control constraints. We show existence and uniqueness of an optimal state–control pair and propose a method to approximate it. Due to the low regularity of the solution to the state equation, rates of convergence cannot be proved unless problematic assumptions are made. Instead, we appeal to the theory of Γ-convergence to show the convergence of our scheme.

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Acknowledgements

E. Otárola was supported in part by CONICYT through FONDECYT project 3160201. A.J. Salgado was supported in part by NSF grant DMS-1418784.

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Authors and Affiliations

  1. Departamento de Matemática, Universidad Técnica Federico Santa María, Valparaíso, Chile

    Enrique Otárola

  2. Department of Mathematics, University of Tennessee, Knoxville, TN, 37996, USA

    Abner J. Salgado

Authors
  1. Enrique Otárola
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  2. Abner J. Salgado
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Corresponding author

Correspondence to Abner J. Salgado .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, George Mason University, Fairfax, VA, USA

    Harbir Antil

  2. Center for Computing Research, Sandia National Laboratories, Albuquerque, NM, USA

    Drew P. Kouri

  3. Corporate Strategic Research, ExxonMobil Research and Engineering Company, Annandale, NJ, USA

    Martin-D. Lacasse

  4. Center for Computing Research, Sandia National Laboratories, Albuquerque, NM, USA

    Denis Ridzal

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Otárola, E., Salgado, A.J. (2018). Optimization of a Fractional Differential Equation. In: Antil, H., Kouri, D.P., Lacasse, MD., Ridzal, D. (eds) Frontiers in PDE-Constrained Optimization. The IMA Volumes in Mathematics and its Applications, vol 163. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-8636-1_8

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