Distributed Solution of Mixed-Integer Programs by ADMM with Closed Duality Gap

This paper introduces a new method to efficiently solve distributed mixed-integer programs (MIP) as arising in problems of distributed machine learning or distributed control. The method is based on the alternating direction method of multipliers (ADMM), and it determines an exact penalty weight in order to close the duality gap of the MIP. The weight, which can be computed with low effort, allows one to formulate and solve a two-stage ADMM procedure for determining an optimum (or a sub-optimum) of the MIP. Numeric examples confirm the efficiency of the proposed method.