A Stabilizing Control Algorithm for Asynchronous Parallel Quadratic Programing via Dual Decomposition

Abstract

This paper proposes a control algorithm for stable implementation of asynchronous parallel quadratic programing (PQP) through a dual decomposition technique. In general, distributed and parallel optimization requires synchronization of data at each iteration step due to the interdependency of data. The synchronization latency may incur a large amount of waiting time caused by an idle process during computation. We aim to mitigate this synchronization penalty in PQP problems by implementing asynchronous updates of the dual variable. The price to pay for adopting asynchronous computing algorithms is the unpredictability of the solution, resulting in a tradeoff between speedup and accuracy. In the worst case, the state of interest may become unstable owing to the stochastic behavior of asynchrony. The stability condition of asynchronous PQP problems is investigated by employing the switched system framework. A formal algorithm is provided to ensure the asymptotic stability of dual variables. Furthermore, it is shown that the implementation of the proposed algorithm guarantees the uniqueness of optimal solutions, irrespective of asynchronous behavior. To verify the validity of the proposed methods, simulation results are presented.