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.
Fractional PDE constrained optimization: Box and sparse constrained problems
Durastante F.;
2018-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.