Min-Sum-Min Message-Passing for Quadratic Optimization

We study the minimization of a quadratic objective function in a distributed fashion. It is known that the min-sum algorithm can be applied to solve the minimization problem if the algorithm converges. We propose a min-summin message-passing algorithm which includes the min-sum algorithm as a special case. As the name suggests, the new algorithm involves two minimizations in each iteration as compared to the min-sum algorithm which has one minimization. The algorithm is derived based on a new closed-loop quadratic optimization problem which has the same optimal solution as the original one. Experiments demonstrate that our algorithm improves the convergence speed of the min-sum algorithm by properly selecting a parameter in the algorithm. Furthermore, we find empirically that in some situations where the minsum algorithm fails, our algorithm still converges to the right solution. Experiments show that if our algorithm converges, our algorithm outperform a reference method with fast convergence speed. Keywords-Distributed optimization, Gaussian belief propagation, message-passing algorithms