确定非线性子扩散方程中非光滑势参数的非光滑优化方法

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-11-09 DOI:10.1016/j.cnsns.2024.108437

A. Oulmelk , L. Afraites , A. Hadri , Mahmoud A. Zaky , A.S. Hendy , Xiangcheng Zheng , Hong Wang

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引用次数: 0

摘要

本文提出了一种通过非光滑最优控制方法利用终端观测确定非线性子扩散模型中的非光滑势参数的方法。方法是将逆问题转换为最优控制问题，成本函数中的保真度和正则化项分别用 L1 和 TV 规范表示，以考虑势的非光滑性。最优控制问题存在一个最小值，并使用基元-二元方法获得了数值解。通过与梯度下降法的数值结果对比，证明了所提方法的有效性。

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Nonsmooth optimization method for determining nonsmooth potential parameter in nonlinear subdiffusion equation

A determination of the nonsmooth potential parameter in a nonlinear subdiffusion model using terminal observation through a nonsmooth optimal control approach is proposed. This is achieved by converting the inverse problem to an optimal control problem with the fidelity and regularization terms in the cost functional represented by the

L^{1}

and TV norms, respectively, in order to account for the nonsmoothness of the potential. The existence of a minimizer for the optimal control problem is established and numerical solutions are obtained using the primal–dual method. The effectiveness of the proposed method is demonstrated via numerical results in comparison with the gradient descent method.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.