Abstract
We analyze a new decomposition approach for convex structured programs based on augmented Lagrangian functions with multiple scaling parameters. We obtain global convergence results with weak hypotheses. Numerical results are presented on a class of multicommodity flow problems; empirical choices of the scaling parameters updates are discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hamdi, A., Mahey, P., and Dussault, J. P., A New Decomposition Method in Nonconvex Progamming via a Separable Augmented Lagrangian, Recent Advances in Optimization, Edited by P. Gritzmann, R. Horst, E. Sachs, and R. Tishchatschke, Lecture Notes in Economics and Mathematical Systems, Springer Verlag, Berlin, Germany, Vol. 452, pp. 90–104, 1997.
P. Mahey S. Oualibouch D. T. Pham (1995) ArticleTitleProximal Decomposition on the Graph of a Maximal Monotone Operator SIAM Journal on Optimization 5 225–236 Occurrence Handle10.1137/0805023
M. Fukushima (1992) ArticleTitleApplication of the Alternating Directions Method of Multipliers to Separable Convex Programming Problems Computational Optimization and Applications 1 83–111 Occurrence Handle10.1007/BF00247655
J. Eckstein (1989) Splitting Methods for Monotone Operators with Applications to Parallel Optimization Department of Civil Engineering Massachusetts, Institute of Technology Cambridge, Massachusetts
Mahey, P., Dussault, J. P., and Hamdi, A., Adaptative Scaling and Convergence Rates of a Separable Augmented Lagrangian Algorithm, Recent Advances in Optimization, Edited by V. H. Nguyen, J. J. Strodiot, and P. Tossings, Lecture Notes in Economics and Mathematical Systems, Springer Verlag, Berlin, Germany, Vol. 481, pp. 278–287, 2000.
A. Ouorou P. Mahey J. P. Vial (2000) ArticleTitleA Survey of Algorithms for Convex Multicommodity Flow Problems Management Science 46 126–147 Occurrence Handle10.1287/mnsc.46.1.126.15132
A. Ouorou (1995) Décomposition Proximale des Problèmes de Multiflot à Critère Convexe: Application aux Problèmes de Routage dans les Réseaux de Communication Université Blaise-Pascal Clermont Ferrand France
Author information
Authors and Affiliations
Additional information
Communicated by J.-P. Crouzeix
The authors gratefully acknowledge the help of J.-P. Crouzeix in simplifying the proof of the main convergence result.
Rights and permissions
About this article
Cite this article
Guèye, O.M., Dussault, J.P. & Mahey, P. Separable Augmented Lagrangian Algorithm with Multidimensional Scaling for Monotropic Programming. J Optim Theory Appl 127, 329–345 (2005). https://doi.org/10.1007/s10957-005-6547-4
Issue Date:
DOI: https://doi.org/10.1007/s10957-005-6547-4