Error Estimates for Fractional Semilinear Optimal Control on Lipschitz Polytopes

Otárola, Enrique

doi:10.1007/s00245-023-10009-1

Cited by 3 publications

(1 citation statement)

References 28 publications

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“…For fractional Laplace operator operators, we usually have two definitions, one is the spectral definition [1, 2, 19, 23], and the other is integral definition [4, 21, 22]. Through literature review, we found that for the optimal control problem of fractional Laplace operator in the spectral definition, a series of works have been developed in recent years based on Caffarelli–Silverstre extension, for example, see [1, 2, 19, 23], etc.…”

Section: Introductionmentioning

confidence: 99%

An efficient and accurate numerical method for the fractional optimal control problems with fractional Laplacian and state constraint

Zhang

Yang

2023

Numerical Methods Partial

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In this paper, we investigate the numerical approximation of an optimal control problem with fractional Laplacian and state constraint in integral form based on the Caffarelli–Silvestre expansion. The first order optimality conditions of the extended optimal control problem is obtained. An enriched spectral Galerkin discrete scheme for the extended problem based on weighted Laguerre polynomials is proposed. A priori error estimate for the enriched spectral discrete scheme is proved. Numerical experiments demonstrate the effectiveness of our method and validate the theoretical results.

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Section: Introductionmentioning

confidence: 99%

An efficient and accurate numerical method for the fractional optimal control problems with fractional Laplacian and state constraint

Zhang

Yang

2023

Numerical Methods Partial

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Optimal control problem with nonlinear fractional system constraint applied to image restoration

Atlas,

Attmani,

Karami

et al. 2024

Math Methods in App Sciences

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This study aims to investigate a novel nonlinear optimization problem that incorporate a partial differential equation (PDE) constraint for image denoising in the context of mixed noise removal. Based on ‐norm and decomposition approach, we develop a nonlinear system that involves the fractional Laplacian operator. Based on Schauder's fixed point theorem, we establish the existence and uniqueness of weak solution for the direct problem. Furthermore, we study the well‐posedness of the optimal control, and we also prove the existence of the weak solutions for the adjoint problem by using Galerkin's method. In order to numerically compute the solution of the proposed model, we introduce the numerical discretization scheme and the primal–dual algorithm used to solve our problem. Finally, we provide comparative numerical experiments to evaluate the efficiency and effectiveness of our proposed model.

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Bilinear Optimal Control for the Fractional Laplacian: Analysis and Discretization

Bersetche,

Fuica,

Otárola

et al. 2024

SIAM J. Numer. Anal.

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Error Estimates for Fractional Semilinear Optimal Control on Lipschitz Polytopes

Cited by 3 publications

References 28 publications

An efficient and accurate numerical method for the fractional optimal control problems with fractional Laplacian and state constraint

An efficient and accurate numerical method for the fractional optimal control problems with fractional Laplacian and state constraint

Optimal control problem with nonlinear fractional system constraint applied to image restoration

Bilinear Optimal Control for the Fractional Laplacian: Analysis and Discretization

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