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In this paper, we extend the bi-alternating direction method of multipliers (BiADMM) designed on a graph of two nodes to a graph of multiple nodes. In particular, we optimize a sum of convex functions defined over a general graph, where every edge carries a linear equality constraint. In designing the new algorithm, an augmented primal-dual Lagrangian function is carefully constructed which naturally...
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...
In this paper we propose a new message-passing algorithm for quadratic optimization. The design of the new algorithm is based on linear coordinate-descent between neighboring nodes. The updating messages are in a form of linear functions as compared to the min-sum algorithm of which the messages are in a form of quadratic functions. Therefore, the linear coordinate-descent (LiCD) algorithm has simpler...
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