  The performance of networks that use the Internet Protocol is sensitive to
precise configuration of many low-level parameters on each network device.
These settings govern the action of dynamic routing protocols, which direct the
flow of traffic; in order to ensure that these dynamic protocols all converge
to produce some 'optimal' flow, each parameter must be set correctly. Multiple
conflicting optimization objectives, nondeterminism, and the need to reason
about different failure scenarios make the task particularly complicated.
  We present a fast and flexible approach for the analysis of a number of such
management tasks presented in the context of BGP routing. The idea is to
combine {\em logical} satisfiability criteria with traditional {\em numerical}
optimization, to reach a desired traffic flow outcome subject to given
constraints on the routing process. The method can then be used to probe
parameter sensitivity, trade-offs in the selection of optimization goals,
resilience to failure, and so forth. The theory is underpinned by a rigorous
abstraction of the convergence of distributed asynchronous message-passing
protocols, and is therefore generalizable to other scenarios. Our resulting
hybrid engine is faster than either purely logical or purely numeric
alternatives, making it potentially feasible for interactive production use.
