Yayınlanmış 1 Ocak 2023 | Sürüm v1
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A stochastic gradient algorithm with momentum terms for optimal control problems governed by a convection-diffusion equation with random diffusivity

  • 1. Middle East Tech Univ, Inst Appl Math, TR-06800 Ankara, Turkiye

Açıklama

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.(c) 2022 Elsevier B.V. All rights reserved.

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