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Zbl 0763.90071
Fukushima, Masao
Application of the alternating direction method of multipliers to separable convex programming problems. (English)
[J] Comput. Optim. Appl. 1, No.1, 93-111 (1992). ISSN 0926-6003; ISSN 1573-2894/e

Summary: 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.

MSC 2000:: *90C25 Convex programming
90-08 Computational methods (optimization)
65Y05 Parallel computation (numerical methods)
49M27 Decomposition methods

Keywords: separable convex programming; parallel algorithm; decomposition algorithm; separable structure; alternating direction method of multipliers; global convergence

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