  Structural discovery amongst a set of variables is of interest in both static
and dynamic settings. In the presence of lead-lag dependencies in the data, the
dynamics of the system can be represented through a structural equation model
(SEM) that simultaneously captures the contemporaneous and temporal
relationships amongst the variables, with the former encoded through a directed
acyclic graph (DAG) for model identification. In many real applications, a
partial ordering amongst the nodes of the DAG is available, which makes it
either beneficial or imperative to incorporate it as a constraint in the
problem formulation. This paper develops an algorithm that can seamlessly
incorporate a priori partial ordering information for solving a linear SEM
(also known as Structural Vector Autoregression) under a high-dimensional
setting. The proposed algorithm is provably convergent to a stationary point,
and exhibits competitive performance on both synthetic and real data sets.
