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In this paper, we propose a distributed algorithm for solving large-scaleseparable convex problems using Lagrangian dual decomposition and theinterior-point framework. By adding self-concordant barrier terms to theordinary Lagrangian, we prove under mild assumptions that the correspondingfamily of augmented dual functions is self-concordant. This makes it possibleto efficiently use the Newton method for tracing the central path. We show thatthe new algorithm is globally convergent and highly parallelizable and thus itis suitable for solving large-scale separable convex problems.

An Interior-Point Lagrangian Decomposition Method for Separable Convex Optimization