An asynchronous Oneshot method with load-balancing
We propose a ‘blurred’ one-shot method for the minimization of design optimization problems using a parallel and asynchronous evaluation of the three basic tasks: the state-, the adjoint- and the control-update. In particular, for each task it is allowed to always use and/or override the latest information of another task, i.e., rather than waiting until the fixed-point iteration provides a new state update it is assumed that parts of the corresponding adjoint iteration already use the latest information from the simulation code. Naturally, this cross-communication between the three tasks will lead to inconsistencies and any mathematical convergence theory for such an approach is far from being obvious.
Nevertheless, one can expect convergence of the method in certain cases. The key for the success of such a method relies on an optimal distribution of the different tasks for a given amount of available resources on a igh performance cluster. This assignment problem yields a possibility to influence the contraction rates of the primal and dual updates as well as the change in the control variables. Also, it can be be shown that the blurred Oneshot algorithm is a generalization of the previously presented Jacobi- and (Multistep-) Seidel-Oneshot method, which can be recovered by a suitable allocation of resources. The blurred method can be applied on (discretized) optimal control problems, which might also include unsteady PDEs.