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Separable augmented Lagrangian algorithm with multidimensional scaling for monotropic programming. (English) Zbl 1116.90105
Summary: 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.
MSC:
90C35Programming involving graphs or networks
90C25Convex programming
90B10Network models, deterministic (optimization)
References:
[1]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.
[2] · Zbl 0834.90105 · doi:10.1137/0805023
[3] · Zbl 0763.90071 · doi:10.1007/BF00247655
[4]
[5]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.
[6] · Zbl 1231.90110 · doi:10.1287/mnsc.46.1.126.15132
[7]