Parareal in time intermediate targets methods for optimal control problem
For researchers working on optimal control of parabolic PDEs, this method enables parallel-in-time computation, but the results are incremental without concrete performance numbers.
The authors present a method to solve the Euler-Lagrange system for optimal control of parabolic equations in parallel, using iterative updates of intermediate targets. Numerical experiments demonstrate efficiency.
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.