  We propose a general framework for solving quantum state estimation problems
using the minimum relative entropy criterion. A convex optimization approach
allows us to decide the feasibility of the problem given the data and, whenever
necessary, to relax the constraints in order to allow for a physically
admissible solution. Building on these results, the variational analysis can be
completed ensuring existence and uniqueness of the optimum. The latter can then
be computed by standard, efficient standard algorithms for convex optimization,
without resorting to approximate methods or restrictive assumptions on its
rank.
