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Fractional PDE constrained optimization: box and sparse constrained problems. (English) Zbl 1416.49033

Falcone, Maurizio (ed.) et al., Numerical methods for optimal control problems. Proceedings of the workshop, Rome, Italy, June 19–23, 2017. Cham: Springer. Springer INdAM Ser. 29, 111-135 (2018).
Summary: 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.
For the entire collection see [Zbl 1411.49002].

MSC:

49M30 Other numerical methods in calculus of variations (MSC2010)
49M15 Newton-type methods
35R11 Fractional partial differential equations

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