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

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 ter...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 422; p. 114919
Main Authors: Toraman, Sıtkı Can, Yücel, Hamdullah
Format: Journal Article
Language:English
Published: Elsevier B.V 01.04.2023
Subjects:
Monte Carlo
PDE-constrained optimization
Stochastic momentum
Uncertainty quantification
35R60
49J20
Monte Carlo
PDE-constrained optimization
Stochastic momentum
Uncertainty quantification
65C05
60H15
60H35
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2022.114919