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28 March 2023 An mADMM-PDAS method for elliptic optimal control problems
Xiaotong Chen
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Proceedings Volume 12597, Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022); 125970U (2023) https://doi.org/10.1117/12.2672293
Event: Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022), 2022, Nanjing, China
Abstract
In this paper, elliptic optimal control problems with 𝐿2-control cost and box constraints on the control are considered. To numerically solve the problems, we apply the First discretize, then optimize approach. Specifically, the standard piecewise linear finite element is employed to discretize the elliptic optimal control problems first. Then, a multilevel Alternating Direction Method of Multipliers (mADMM) is proposed to obtain approximate solutions with medium accuracy. Finally, the Primal-Dual Active Set (PDAS) method is used as a postprocessor of the mADMM method to obtain more accurate solutions. Based on the strategies above, an efficient two-phase mADMM-PDAS method is proposed. Numerical results show that the mADMM-PDAS method is highly efficient.
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Xiaotong Chen "An mADMM-PDAS method for elliptic optimal control problems", Proc. SPIE 12597, Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022), 125970U (28 March 2023); https://doi.org/10.1117/12.2672293
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KEYWORDS
Numerical analysis
Mathematical optimization
MATLAB
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