  Estimation of nonlinear dynamic models from data poses many challenges,
including model instability and non-convexity of long-term simulation fidelity.
Recently Lagrangian relaxation has been proposed as a method to approximate
simulation fidelity and guarantee stability via semidefinite programming (SDP),
however the resulting SDPs have large dimension, limiting their utility in
practical problems. In this paper we develop a path-following interior point
algorithm that takes advantage of special structure in the problem and reduces
computational complexity from cubic to linear growth with the length of the
data set. The new algorithm enables empirical comparisons to established
methods including Nonlinear ARX, and we demonstrate superior generalization to
new data. We also explore the "regularizing" effect of stability constraints as
an alternative to regressor subset selection.
