PARAOPT: A parareal algorithm for optimality systems

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