Application of a smoothing technique to decomposition in convex optimization

Dual decomposition is a powerful technique for deriving decomposition schemes for convex optimization problems with specific structure. Although the Augmented Lagrangian is computationally more stable than the ordinary Lagrangian, the \textit{prox-term} destroys the separability of the given problem. In this paper we use another approach to obtain a smooth Lagrangian, based on a smoothing technique … Read more

An interior-point Lagrangian decomposition method for separable convex optimization

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 … Read more