Generalized linear coordinate-descent message-passing for convex optimization

In this paper we propose a generalized linear coordinate-descent (GLiCD) algorithm for a class of unconstrained convex optimization problems. The considered objective function can be decomposed into edge-functions and node-functions of a graphical model. The messages of the GLiCD algorithm are in a form of linear functions, as compared to the min-sum algorithm of which the form of messages depends on the objective function. Thus, the implementation of the GLiCD algorithm is much simpler than that of the min-sum algorithm. A theorem is stated according to which the algorithm converges to the optimal solution if the objective function satisfies a diagonal-dominant condition. As an application, the GLiCD algorithm is exploited in solving the averaging problem in sensor networks, where the performance is compared to that of the min-sum algorithm.