  In this paper, we analyze the convergence as well as the rate of convergence
of asynchronous distributed quadratic programming (QP) with dual decomposition
technique. In general, distributed optimization requires synchronization of
data at each iteration step due to the interdependency of data. This
synchronization latency may incur a large amount of waiting time caused by an
idle process during computation. We aim to attack this synchronization penalty
in distributed QP problems by implementing asynchronous update of dual
variable. The price to pay for adopting asynchronous computing algorithms is
unpredictability of the solution, resulting in a tradeoff between speedup and
accuracy. Thus, the convergence to an optimal solution is not guaranteed owing
to the stochastic behavior of asynchrony. In this paper, we employ the switched
system framework as an analysis tool to investigate the convergence of
asynchronous distributed QP. This switched system will facilitate analysis on
asynchronous distributed QP with dual decomposition, providing necessary and
sufficient conditions for the mean square convergence. Also, we provide an
analytic expression for the rate of convergence through the switched system,
which enables performance analysis of asynchronous algorithms as compared with
synchronous case. To verify the validity of the proposed methods, numerical
examples are presented with an implementation of asynchronous parallel QP using
OpenMP.
