Convergence of generalized linear coordinate-descent message-passing for quadratic optimization

We study the generalized linear coordinate-descent (GLiCD) algorithm for the quadratic optimization problem. As an extension of the linear coordinate-descent (LiCD) algorithm, the GLiCD algorithm incorporates feedback from last iteration in generating new messages. We show that if the amount of feedback signal from last iteration is above a threshold and the GLiCD algorithm converges, it computes the optimal solution. Based on the result, we further show that if the feedback signal is large enough, the GLiCD algorithm is guaranteed to converge.