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In this paper we propose an efficient distributed algorithm for solvingloosely coupled convex optimization problems. The algorithm is based on aprimal-dual interior-point method in which we use the alternating directionmethod of multipliers (ADMM) to compute the primal-dual directions at eachiteration of the method. This enables us to join the exceptional convergenceproperties of primal-dual interior-point methods with the remarkableparallelizability of ADMM. The resulting algorithm has superior computationalproperties with respect to ADMM directly applied to our problem. The amount ofcomputations that needs to be conducted by each computing agent is far less. Inparticular, the updates for all variables can be expressed in closed form,irrespective of the type of optimization problem. The most expensivecomputational burden of the algorithm occur in the updates of the primalvariables and can be precomputed in each iteration of the interior-pointmethod. We verify and compare our method to ADMM in numerical experiments.

A distributed primal-dual interior-point method for loosely coupled problems using ADMM