  In this paper, we propose two exact distributed algorithms to solve mixed
integer linear programming (MILP) problems with multiple agents where data
privacy is important for the agents. A key challenge is that, because of the
non-convex nature of MILPs, classical distributed and decentralized
optimization approaches cannot be applied directly to find their optimal
solutions. The proposed exact algorithms are based on adding primal cuts and
restricting the Lagrangian relaxation of the original MILP problem. We show
finite convergence of these algorithms for MILPs with only binary and
continuous variables. We test the proposed algorithms on the unit commitment
problem and discuss its pros and cons comparing to the central MILP approach.
