Abstract

The time parallel solution of optimality systems arising in PDE constrained optimization could be achieved by simply applying any time parallel algorithm, such as Parareal, to solve the forward and backward evolution problems arising in the optimization loop. We propose here a different strategy by devising directly a new time parallel algorithm, which we call ParaOpt, for the coupled forward and backward nonlinear partial differential equations. ParaOpt is inspired by the Parareal algorithm for evolution equations and thus is automatically a two-level method. We provide a detailed convergence analysis for the case of linear parabolic PDE constraints. We illustrate the performance of ParaOpt with numerical experiments for both linear and nonlinear optimality systems.

Keywords

  1. Parareal algorithm
  2. optimal control
  3. preconditioning

MSC codes

  1. 49M27
  2. 68W10
  3. 65K10
  4. 65F08
  5. 93B40

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Information & Authors

Information

Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: A2773 - A2802
ISSN (online): 1095-7197

History

Submitted: 9 October 2019
Accepted: 6 July 2020
Published online: 17 September 2020

Keywords

  1. Parareal algorithm
  2. optimal control
  3. preconditioning

MSC codes

  1. 49M27
  2. 68W10
  3. 65K10
  4. 65F08
  5. 93B40

Authors

Affiliations

Funding Information

Agence Nationale de la Recherche https://doi.org/10.13039/501100001665 : ANR-15-CE23-0019, ANR-19-CE46-0013/A-HKBU203/19

Funding Information

Research Grants Council, University Grants Committee https://doi.org/10.13039/501100002920 : ECS 22300115, GRF 12301817

Funding Information

Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung https://doi.org/10.13039/501100001711 : 200020_178752

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