Parareal in time intermediate targets methods for optimal control   problem
  In this paper, we present a method that enables solving in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets that gives rise to independent sub-problems that can be solved in parallel. This method can be coupled with the parareal in time algorithm. Numerical experiments show the efficiency of our method. 
Yvon Maday, Mohamed-Kamel Riahi, Julien Salomon
math.OC math.NA