Find out how to access previewonly content
Application of the alternating direction method of multipliers to separable convex programming problems
 Masao Fukushima
 … show all 1 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
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.
 Bertsekas, D.P. (1982) Constrained Optimization and Lagrange Multiplier Methods. Academic Press, New York
 Bertsekas, D.P., Tsitsiklis, J.N. (1989) Parallel and Distributed Computation: Numerical Methods. PrenticeHall, Englewood Cliffs, NJ
 Fortin, M., Glowinski, R. On decompositioncoordination methods using an augmented Lagrangian. In: Fortin, M., Glowinski, R. eds. (1983) Augmented Lagrangian Methods: Applications to the Numerical Solution of BoundaryValue Problems. NorthHolland, Amsterdam, pp. 97146
 Gabay, D., Mercier, B. (1976) A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Comput. Math. App., 2: pp. 1740
 Lasdon, L.S. (1970) Optimization Theory for Large Systems. Macmillan, New York
 LemarĂ©chal, C. Nondifferentiable optimization. In: Nemhauser, G.L., Rinnooy Kan, A.H.G., Todd, M.J. eds. (1989) Handbooks in Operations Research and Management Science, Vol. 1, Optimization. NorthHolland, Amsterdam, pp. 529572
 Rockafellar, R.T. (1970) Convex Analysis. Princeton University Press, Princeton, NJ
 Rockafellar, R.T. (1976) Monotone operators and the proximal point algorithm. SIAM J. on Control and Optimization 14: pp. 877898
 Rockafellar, R.T. (1976) Augmented Lagrangians and applications of the proximal point algorithm in convex programming. Math. of Oper. Res. 1: pp. 97116
 Spingarn, J.E. (1983) Partial inverse of a monotone operator. Appl. Math. and Optimization 10: pp. 247265
 Spingarn, J.E. (1985) Applications of the method of partial inverses to convex programming: Decomposition. Math. Programming 32: pp. 199223
 Tseng, P. (1990) Dual ascent methods for problems with strictly convex costs and linear constraints: A unified approach. SIAM J. on Control and Optimization 28: pp. 214242
 Tseng, P. (1990) Further applications of a splitting algorithm to decomposition in variational inequalities and convex programming. Math. Programming 48: pp. 249263
 Tseng, P. (1991) Applications of a splitting algorithm to decomposition in convex programming and variational inequalities. SIAM J. on Control and Optimization 29: pp. 119138
 Wets, R.J.B. Convergence of convex functions, variational inequalities and convex optimization problems. In: Cottle, R.W., Giannessi, F., Lions, J.L. eds. (1980) Variational Inequalities and Complementarity Problems. John Wiley, Chichester, U.K., pp. 375403
 Title
 Application of the alternating direction method of multipliers to separable convex programming problems
 Journal

Computational Optimization and Applications
Volume 1, Issue 1 , pp 93111
 Cover Date
 19921001
 DOI
 10.1007/BF00247655
 Print ISSN
 09266003
 Online ISSN
 15732894
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Convex programming
 separable problems
 decomposition
 alternating direction method of multipliers
 parallel algorithm
 Industry Sectors
 Authors

 Masao Fukushima ^{(1)}
 Author Affiliations

 1. Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, 606, Kyoto, Japan