Paraopt: A parareal algorithm for optimality systems

Martin J. Gander, Felix Kwok, Julien Salomon

Research output: Contribution to journalJournal articlepeer-review

16 Citations (Scopus)
21 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)A2773-A2802
Number of pages30
JournalSIAM Journal on Scientific Computing
Issue number5
Publication statusPublished - 17 Sept 2020

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Optimal control
  • Parareal algorithm
  • Preconditioning


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