  We develop a decomposition algorithm for distributionally-robust two-stage
stochastic mixed-integer convex cone programs, and its important special case
of distributionally-robust two-stage stochastic mixed-integer second order cone
programs. This generalizes the algorithm proposed by Sen and
Sherali~[Mathematical Programming 106(2): 203-223, 2006]. We show that the
proposed algorithm is finitely convergent if the second-stage problems are
solved to optimality at incumbent first stage solutions, and solution to an
optimization problem to identify worst-case probability distribution is
available. The second stage problems can be solved using a branch-and-cut
algorithm. The decomposition algorithm is illustrated with an example.
Computational results on a stochastic programming generalization of a facility
location problem show significant solution time improvements from the proposed
approach. Solutions for many models that are intractable for an extensive form
formulation become possible. Computational results suggest that solution time
requirement does not increase significantly when considering distributional
robust counterparts to the stochastic programming models.
