Volume 13, Issue 4
Finite Element Approximation of Space Fractional Optimal Control Problem with Integral State Constraint

Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 1027-1049.

Published online: 2020-06

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• Abstract

In this paper finite element approximation of space fractional optimal control problem with integral state constraint is investigated. First order optimal condition and regularity of the control problem are discussed. A priori error estimates for control, state, adjoint state and lagrange multiplier are derived. The nonlocal property of the fractional derivative results in a dense coefficient matrix of the discrete state and adjoint state equation. To reduce the computational cost a fast projection gradient algorithm is developed based on the Toeplitz structure of the coefficient matrix. Numerical experiments are carried out to illustrate the theoretical findings.

• Keywords

Finite element method, optimal control problem, state constraint, space fractional equation, a priori error estimate, fast algorithm.

65N30

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@Article{NMTMA-13-1027, author = {Zhaojie Zhou , and Jiabin Song , and Yanping Chen , }, title = {Finite Element Approximation of Space Fractional Optimal Control Problem with Integral State Constraint}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2020}, volume = {13}, number = {4}, pages = {1027--1049}, abstract = {

In this paper finite element approximation of space fractional optimal control problem with integral state constraint is investigated. First order optimal condition and regularity of the control problem are discussed. A priori error estimates for control, state, adjoint state and lagrange multiplier are derived. The nonlocal property of the fractional derivative results in a dense coefficient matrix of the discrete state and adjoint state equation. To reduce the computational cost a fast projection gradient algorithm is developed based on the Toeplitz structure of the coefficient matrix. Numerical experiments are carried out to illustrate the theoretical findings.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2019-0201}, url = {http://global-sci.org/intro/article_detail/nmtma/16965.html} }
TY - JOUR T1 - Finite Element Approximation of Space Fractional Optimal Control Problem with Integral State Constraint AU - Zhaojie Zhou , AU - Jiabin Song , AU - Yanping Chen , JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 1027 EP - 1049 PY - 2020 DA - 2020/06 SN - 13 DO - http://doi.org/10.4208/nmtma.OA-2019-0201 UR - https://global-sci.org/intro/article_detail/nmtma/16965.html KW - Finite element method, optimal control problem, state constraint, space fractional equation, a priori error estimate, fast algorithm. AB -

In this paper finite element approximation of space fractional optimal control problem with integral state constraint is investigated. First order optimal condition and regularity of the control problem are discussed. A priori error estimates for control, state, adjoint state and lagrange multiplier are derived. The nonlocal property of the fractional derivative results in a dense coefficient matrix of the discrete state and adjoint state equation. To reduce the computational cost a fast projection gradient algorithm is developed based on the Toeplitz structure of the coefficient matrix. Numerical experiments are carried out to illustrate the theoretical findings.

Zhaojie Zhou, Jiabin Song & Yanping Chen. (2020). Finite Element Approximation of Space Fractional Optimal Control Problem with Integral State Constraint. Numerical Mathematics: Theory, Methods and Applications. 13 (4). 1027-1049. doi:10.4208/nmtma.OA-2019-0201
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