Distributed Optimization for Mixed-Integer Consensus in Multi-Agent Networks

This paper considers the consensus of mixed-integer linear programming (MILP) problems as occurring in distributed control and machine learning of multi-agent networks. Unlike existing work on consensus problems, in which the agents only have to agree on the continuous part of their decision variables, this paper proposes a new method to enable them to also agree on the integer part. This mixed-integer setting may arise from distributed control problems of hybrid dynamical systems, or distributed machine learning problems using support vector machines. It is shown in this paper that the consensus of mixed-integer variables is guaranteed to be achieved by a tailored series of continuous consensus problems.