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

TORAMAN S. C., YÜCEL H.

Journal of Computational and Applied Mathematics, vol.422, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 422
  • Publication Date: 2023
  • Doi Number: 10.1016/j.cam.2022.114919
  • Journal Name: Journal of Computational and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
  • Keywords: Monte Carlo, PDE-constrained optimization, Stochastic momentum, Uncertainty quantification
  • Middle East Technical University Affiliated: Yes

Abstract

© 2022 Elsevier B.V.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.