Linear convergence of distributed multiple shooting

Distributed multiple shooting is a modification of the multiple shooting approach for discretizing optimal control problems wherein the separate components of a large-scale system are discretized as well as shooting time intervals. In an SQP algorithm that solves the resulting discretized nonlinear program, the adjoint based version of the algorithm additionally discards certain derivatives appearing in the resulting quadratic programs in order to lead to computational savings in sensitivity generation and solving the QP. It was conjectured that adjoint-based distributed multiple shooting behaves like an inexact SQP method and converges linearly to the optimal solution, provided that the discarded derivatives are sufficiently uninfluential in the total dynamics of the system. This paper confirms this conjecture theoretically by providing the appropriate convergence theory, as well as numerically, by analyzing the convergence properties of the algorithm as applied to a problem involving detection of the source of smoke within a set of rooms.