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Journal of Scientific Computing

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14-11-2015

A Fast Gradient Projection Method for a Constrained Fractional Optimal Control

Authors: Ning Du, Hong Wang, Wenbin Liu

Published in: Journal of Scientific Computing | Issue 1/2016

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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 \(O(M N^3)\) of a conventional solver to \(O(M N\log N)\) and memory requirement from \(O(N^2)\) to O(N) for a problem of size N and of M time steps. Numerical experiments show the utility of the method.

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Title: A Fast Gradient Projection Method for a Constrained Fractional Optimal Control
Authors: Ning Du
Hong Wang
Wenbin Liu
Publication date: 14-11-2015
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 1/2016
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-015-0125-1

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