In multiuser information theory, there are some rate regions that are fully characterized in terms of mutual 
informations involving auxiliary random variables, and there are some regions for which only inner and outer 
bounds are known.  In either case, computation of the regions is challenging.  Each point on the boundary of a
region corresponds to a solution of an optimization problem of minimizing (for data compression) or maximizing (for 
data transmission) one mutual information subject to constraints on other mutual informations.  These points may be 
computed using alternating minimization algorithms that use variational representations of mutual information 
introduced by O’Sullivan at ITA in 2009.  This method is applied to computing outer (Berger-Tung) bounds for the 
distributed source coding region.  At any point, only two of the rate constraints can be active at a time, so the 
corresponding optimization is a tradeoff between the two constraints and is implemented using a Lagrange multiplier.  
Distortion constraints are implemented using Lagrange multipliers.  For each choice of Lagrange multipliers, the 
corresponding alternating minimization algorithm has been implemented in Matlab.  The computations are linear in 
the dimension of the space of variables per iteration, rather than existing algorithms that are exponential in this 
dimension.  Implementations on a few standard discrete source models and distortion functions are described.  
Interpretation of the implications of the results is ongoing.