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Application of a smoothing technique to decomposition in convex optimization

Ion Necoara(ion.necoara***at***esat.kuleuven.be)
Johan Suykens(johan.suykens***at***esat.kuleuven.be)

Abstract: 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 developed by Nesterov, which preserves separability of the problem. With this approach we derive a new decomposition method, 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. This can be achieved with the new decomposition algorithm since the resulting dual function has good smoothness properties and since we make use of the particular structure of the corresponding problem.

Keywords: Smooth convex minimization, dual decomposition, parallel algorithms, distributed agents, coordination.

Category 1: Convex and Nonsmooth Optimization

Category 2: Applications -- Science and Engineering

Citation: I. Necoara and J. Suykens, ``Application of a smoothing technique to decomposition in convex optimization'', IEEE Transactions on Automatic Control, Vol 53, nr. 11, 2008.

Download: [PDF]

Entry Submitted: 02/04/2009
Entry Accepted: 02/04/2009
Entry Last Modified: 02/04/2009

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