Application of a Smoothing Technique to Decomposition in Convex Optimization

Provided by: Institute of Electrical & Electronic Engineers
Topic: Mobility
Format: PDF
Dual decomposition is a powerful technique for deriving decomposition schemes for convex optimization problems with separable structure. Although the Augmented Lagrangian is computationally more stable than the ordinary Lagrangian, the prox-term destroys the separability of the given problem. In this paper, the authors use another approach to obtain a smooth Lagrangian, based on a smoothing technique developed by Nesterov, which preserves separability of the problem. With this approach they derive a new decomposition method, called proximal center algorithm, which from the viewpoint of efficiency estimates improves the bounds on the number of iterations of the classical dual gradient scheme by an order of magnitude.

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