  Saddle-point or primal-dual methods have recently attracted renewed interest
as a systematic technique to design distributed algorithms which solve convex
optimization problems. When implemented online for streaming data or as dynamic
feedback controllers, these algorithms become subject to disturbances and
noise; convergence rates provide incomplete performance information, and
quantifying input-output performance becomes more important. We analyze the
input-output performance of the continuous-time saddle-point method applied to
linearly constrained quadratic programs, providing explicit expressions for the
saddle-point H2 norm under a relevant input-output configuration. We then
proceed to derive analogous results for regularized and augmented versions of
the saddle-point algorithm. We observe some rather peculiar effects -- a modest
amount of regularization significantly improves the transient performance,
while augmentation does not necessarily offer improvement. We then propose a
distributed dual version of the algorithm which overcomes some of the
performance limitations imposed by augmentation. Finally, we apply our results
to a resource allocation problem to compare the input-output performance of
various centralized and distributed saddle-point implementations and show that
distributed algorithms may perform as well as their centralized counterparts.
