Year: 2020
Communications in Computational Physics, Vol. 27 (2020), Iss. 3 : pp. 753–774
Abstract
In this work, we study a distributed optimal control problem, in which the governing system is given by second-order elliptic equations with log-normal coefficients. To lessen the curse of dimensionality that originates from the representation of stochastic coefficients, the Monte Carlo finite element method is adopted for numerical discretization where a large number of sampled constraints are involved. For the solution of such a large-scale optimization problem, stochastic gradient descent method is widely used but has slow convergence asymptotically due to its inherent variance. To remedy this problem, we adopt an averaged stochastic gradient descent method which performs stably even with the use of relatively large step sizes and small batch sizes. Numerical experiments are carried out to validate our theoretical findings.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2018-0295
Communications in Computational Physics, Vol. 27 (2020), Iss. 3 : pp. 753–774
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: PDE-constrained elliptic control high-dimensional random inputs Monte Carlo finite element stochastic gradient descent.
Author Details
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