In this paper we propose a distributed algorithm for solving large-scale separable convex problems using Lagrangian dual decomposition and the interior-point framework. By adding self-concordant barrier terms to the ordinary Lagrangian we prove under mild assumptions that the corresponding family of augmented dual functions is self-concordant. This makes it possible to efficiently use the Newton method for tracing the central path. We show that the new algorithm is globally convergent and highly parallelizable and thus it is suitable for solving large-scale separable convex problems.
Necoara I., Suykens J.A.K., An interior-point Lagrangian decomposition method for separable convex optimization'', Internal Report 08-150, ESAT-SISTA, K.U.Leuven (Leuven, Belgium), September 2008.