  Several problems in modeling and control of stochastically-driven dynamical
systems can be cast as regularized semi-definite programs. We examine two such
representative problems and show that they can be formulated in a similar
manner. The first, in statistical modeling, seeks to reconcile observed
statistics by suitably and minimally perturbing prior dynamics. The second
seeks to optimally select a subset of available sensors and actuators for
control purposes. To address modeling and control of large-scale systems we
develop a unified algorithmic framework using proximal methods. Our customized
algorithms exploit problem structure and allow handling statistical modeling,
as well as sensor and actuator selection, for substantially larger scales than
what is amenable to current general-purpose solvers. We establish linear
convergence of the proximal gradient algorithm, draw contrast between the
proposed proximal algorithms and alternating direction method of multipliers,
and provide examples that illustrate the merits and effectiveness of our
framework.
