A stochastic gradient algorithm with momentum terms for optimal control problems governed by a convection–diffusion equation with random diffusivity

Date

2023-04-01

Author

Toraman, Sıtkı Can
Yücel, Hamdullah

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In this paper, we focus on a numerical investigation of a strongly convex and smooth optimization problem subject to a convection–diffusion equation with uncertain terms. Our approach is based on stochastic approximation where true gradient is replaced by a stochastic ones with suitable momentum term to minimize the objective functional containing random terms. A full error analysis including Monte Carlo, finite element, and stochastic momentum gradient iteration errors is done. Numerical examples are presented to illustrate the performance of the proposed stochastic approximations in the PDE-constrained optimization setting.

Subject Keywords

Monte Carlo, PDE-constrained optimization, Stochastic momentum, Uncertainty quantification

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85142122266&origin=inward
https://hdl.handle.net/11511/101662

Journal

Journal of Computational and Applied Mathematics

DOI

https://doi.org/10.1016/j.cam.2022.114919

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

S. C. Toraman and H. Yücel, “A stochastic gradient algorithm with momentum terms for optimal control problems governed by a convection–diffusion equation with random diffusivity,” Journal of Computational and Applied Mathematics, vol. 422, pp. 0–0, 2023, Accessed: 00, 2023. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85142122266&origin=inward.