# Application of the alternating direction method of multipliers to separable convex programming problems

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## Abstract

This paper presents a decomposition algorithm for solving convex programming problems with separable structure. The algorithm is obtained through application of the alternating direction method of multipliers to the dual of the convex programming problem to be solved. In particular, the algorithm reduces to the ordinary method of multipliers when the problem is regarded as nonseparable. Under the assumption that both primal and dual problems have at least one solution and the solution set of the primal problem is bounded, global convergence of the algorithm is established.

## Keywords

Convex programming separable problems decomposition alternating direction method of multipliers parallel algorithm## Preview

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© Kluwer Academic Publishers 1992