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A survey on dual decomposition methods

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Abstract

This paper presents decomposition/coordination methods in which the coordination step is ensured by a Lagrange multiplier. The problem must be reformulated as a constrained convex minimization problem by introducing a suitable auxiliary unknown. The role of the auxiliary unknown is to ensure the splitting of the problem according to certain properties (linear/nonlinear, smooth/nonsmooth) or size (domain decomposition). The Lagrange multiplier, for the coordination step, is associated with the continuity condition. The resulting dual (Uzawa) algorithm replaces the original problem by a sequence of subproblems of smaller size or easier to solve.

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  1. LIMOS, Université Blaise Pascal, CNRS UMR 6158, ISIMA, Campus des Cézeaux, BP 10125, 63173 , Aubière Cedex, France

    Jonas Koko

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Koko, J. A survey on dual decomposition methods. SeMA 62, 27–59 (2013). https://doi.org/10.1007/s40324-013-0007-0

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