  We propose a new distributed algorithm for computing a truncated Newton
method, where the main diagonal of the Hessian is computed using belief
propagation. As a case study for this approach, we examine the sensor selection
problem, a Boolean convex optimization problem. We form two distributed
algorithms. The first algorithm is a distributed version of the interior point
method by Joshi and Boyd, and the second algorithm is an order of magnitude
faster approximation. As an example application we discuss distributed anomaly
detection in networks. We demonstrate the applicability of our solution using
both synthetic data and real traffic logs collected from the Abilene Internet
backbone.
