Finite Element Approximation of Space Fractional Optimal Control Problem with Integral State Constraint |
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Authors: | Zhaojie Zhou Jiabin Song & Yanping Chen |
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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. |
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Keywords: | Finite element method optimal control problem state constraint space fractional equation a priori error estimate fast algorithm |
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