A Decomposition Method Based On The Augmented Lagrangian

AbstractIn this paper, we explore the use of the augmented Lagrangian in a decomposition method which is a direct application of the “method of multipliers”. Contrary to popular opinion, the use of the augmented Lagrangian does not necessarily destroy separability inherent in a problem. This separability can be recovered by the use of sequential linearization algorithms, of which the Frank-Wolfe algorithm is an example. We outline this decomposition approach in a fairly general framework and then specialize it to the decomposition of linear programs. Linear programs are, in at least one sense, the worst case for a method of multipliers approach since little is known about the rate of convergence of the dual multipliers in tMs case. We report some computational evidence from two linear programming problems related to forest management which indicates that empirical convergence rates can be quite satisfactory.