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A Fast Gradient Projection Method for a Constrained Fractional Optimal Control

Du, Ning, Wang, Hong, Liu, Wenbin (2015) A Fast Gradient Projection Method for a Constrained Fractional Optimal Control. Journal of Scientific Computing, 68 (1). pp. 1-20. ISSN 0885-7474. E-ISSN 1573-7691. (doi:10.1007/s10915-015-0125-1) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
https://doi.org/10.1007/s10915-015-0125-1

Abstract

Optimal control problems governed by a fractional diffusion equation tends to provide a better description than one by a classical second-order Fickian diffusion equation in the context of transport or conduction processes in heterogeneous media. However, the fractional control problem introduces significantly increased computational complexity and storage requirement than the corresponding classical control problem, due to the nonlocal nature of fractional differential operators. We develop a fast gradient projection method for a pointwise constrained optimal control problem governed by a time-dependent space-fractional diffusion equation, which requires the computational cost from O(MN3)O(MN3) of a conventional solver to O(MNlogN)O(MNlog?N) and memory requirement from O(N2)O(N2) to O(N) for a problem of size N and of M time steps. Numerical experiments show the utility of the method.

Item Type: Article
DOI/Identification number: 10.1007/s10915-015-0125-1
Uncontrolled keywords: Constrained optimal control, Fractional diffusion equation, Fast Fourier transform, Preconditioned conjugate gradient method
Subjects: Q Science
T Technology
Divisions: Faculties > Social Sciences > Kent Business School
Faculties > Social Sciences > Kent Business School > Management Science
Depositing User: Steve Wenbin Liu
Date Deposited: 08 Jun 2017 09:20 UTC
Last Modified: 29 May 2019 19:07 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/61989 (The current URI for this page, for reference purposes)
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