Fractional PDE constrained optimization: box and sparse constrained problems
Fractional PDE constrained optimization: box and sparse constrained problems
In this paper we address the numerical solution of two Fractional Partial Differential Equation constrained optimization problems: the two-dimensional semilinear Riesz Space Fractional Diffusion equation with box or sparse constraints. Both a theoretical and experimental analysis of the problems is carried out. The algorithmic framework is based on the L-BFGS-B method coupled with a Krylov subspace solver for the box constrained problem within an optimize-then-discretize approach and on the semismooth Newton–Krylov method for the sparse one. Suitable preconditioning strategies by approximate inverses and Generalized Locally Toeplitz sequences are taken into account. The numerical experiments are performed with benchmarked software/libraries enforcing the reproducibility of the results.
Constrained optimization, Fractional differential equation, Preconditioner, Saddle matrix
111-135
Durastante, Fabio
56118788-83b2-4273-b959-c45f486f86c1
Cipolla, Stefano
373fdd4b-520f-485c-b36d-f75ce33d4e05
Durastante, Fabio
56118788-83b2-4273-b959-c45f486f86c1
Cipolla, Stefano
373fdd4b-520f-485c-b36d-f75ce33d4e05
Durastante, Fabio and Cipolla, Stefano
(2019)
Fractional PDE constrained optimization: box and sparse constrained problems.
In,
Springer INdAM Series.
(Springer INdAM Series, 29)
Springer Cham, .
(doi:10.1007/978-3-030-01959-4_6).
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Abstract
In this paper we address the numerical solution of two Fractional Partial Differential Equation constrained optimization problems: the two-dimensional semilinear Riesz Space Fractional Diffusion equation with box or sparse constraints. Both a theoretical and experimental analysis of the problems is carried out. The algorithmic framework is based on the L-BFGS-B method coupled with a Krylov subspace solver for the box constrained problem within an optimize-then-discretize approach and on the semismooth Newton–Krylov method for the sparse one. Suitable preconditioning strategies by approximate inverses and Generalized Locally Toeplitz sequences are taken into account. The numerical experiments are performed with benchmarked software/libraries enforcing the reproducibility of the results.
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e-pub ahead of print date: 26 January 2019
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© Springer Nature Switzerland AG 2018.
Keywords:
Constrained optimization, Fractional differential equation, Preconditioner, Saddle matrix
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Local EPrints ID: 485628
URI: http://eprints.soton.ac.uk/id/eprint/485628
ISSN: 2281-518X
PURE UUID: a00a64c4-8938-47d3-88ef-2d0d3bb994cf
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Date deposited: 12 Dec 2023 17:35
Last modified: 18 Mar 2024 04:17
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Author:
Fabio Durastante
Author:
Stefano Cipolla
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