  Lagrangian duality in mixed integer optimization is a useful framework for
problems decomposition and for producing tight lower bounds to the optimal
objective, but in contrast to the convex counterpart, it is generally unable to
produce optimal solutions directly. In fact, solutions recovered from the dual
may be not only suboptimal, but even infeasible. In this paper we concentrate
on large scale mixed--integer programs with a specific structure that is of
practical interest, as it appears in a variety of application domains such as
power systems or supply chain management. We propose a solution method for
these structures, in which the primal problem is modified in a certain way,
guaranteeing that the solutions produced by the corresponding dual are feasible
for the original unmodified primal problem. The modification is simple to
implement and the method is amenable to distributed computations. We also
demonstrate that the quality of the solutions recovered using our procedure
improves as the problem size increases, making it particularly useful for large
scale instances for which commercial solvers are inadequate. We illustrate the
efficacy of our method with extensive experimentations on a problem stemming
from power systems.
