Bundle-based decomposition : conditions for convergence
Robinson, S. M.
Annales de l'I.H.P. Analyse non linéaire, Tome S6 (1989), p. 435-447 / Harvested from Numdam
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Publié le : 1989-01-01
@article{AIHPC_1989__S6__435_0,
     author = {Robinson, S. M.},
     title = {Bundle-based decomposition : conditions for convergence},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {S6},
     year = {1989},
     pages = {435-447},
     mrnumber = {1204026},
     zbl = {0675.90068},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1989__S6__435_0}
}

Robinson, S. M. Bundle-based decomposition : conditions for convergence. Annales de l'I.H.P. Analyse non linéaire, Tome S6 (1989) pp. 435-447. http://gdmltest.u-ga.fr/item/AIHPC_1989__S6__435_0/

[1] H. Brézis, Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert, North-Holland Mathematics Studies No. 5 (North-Holland, Amsterdam, 1973). | MR 348562 | Zbl 0252.47055

[2] H. Brézis and A. Haraux, "Image d'une somme d'opérateurs monotones et applications," Israel Journal of Mathematics 23 (1976) 165-186. | MR 399965 | Zbl 0323.47041

[3] J.K. Ho and E. Loute, "An advanced implementation of the Dantzig-Wolfe decomposition algorithm for linear programming," in: G. B. Dantzig, M. A. H. Dempster, and M. Kallio, eds., Large-Scale Linear Programming (International Institute for Applied Systems Analysis, Laxenburg, Austria, 1981) 425-460. | MR 612625 | Zbl 0539.90063

[4] J.K. Ho and E. Loute, "DECOMP User's Guide," unpublished manuscript.

[5] T. Kato, "Demicontinuity, hemicontinuity, and monotonicity," Bull. Amer. Math. Soc. 70 (1964) 548-550. | MR 163198 | Zbl 0123.10701

[6] T. Kato, "Demicontinuity, hemicontinuity, and monotonicity. II," Bull. Amer. Math. Soc. 73 (1967) 886-889. | MR 238135 | Zbl 0184.36504

[7] C. Lemaréchal, J .-J. Strodiot, and A. Bihain, "On a bundle algorithm for nons-mooth optimization," in: O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, eds., Nonlinear Programming 4 (Academic Press, New York, 1981) 245-282. | MR 663383 | Zbl 0533.49023

[8] L. Mclinden and R.C. Bergstrom, "Preservation of convergence of convex sets and functions in finite dimensions," Trans. Amer. Math. Soc. 268 (1981) 127-142. | MR 628449 | Zbl 0468.90063

[9] D. Medhi, "Decomposition of structured large scale optimization problems and parallel computing," Dissertation, Computer Sciences Department, University of Wisconsin- Madison (Madison, WI 53706, 1987). See also two July 1988 manuscripts by this author: "Bundle-based decomposition for structured large-scale convex optimization problems: error estimate and computational experience," and "Parallel bundlebased decomposition for large-scale structured mathematical programming problems," AT&T Bell Laboratories, Holmdel, NJ 07733.

[10] B.A. Murtagh and M.A. Saunders, "MINOS 5.0 User's Guide," Technical Report No. SOL 83-20, Systems Optimization Laboratory, Department of Operations Research, Stanford University (Stanford, CA 94305, December 1983).

[11] S.M. Robinson, "Bundle-based decomposition: Description and preliminary results," in: A. Prékopa, J. Szelezsán, and B. Strazicky, eds., System Modelling and Optimization (Lecture Notes in Control and Information Sciences No. 84, Springer-Verlag, Berlin, 1986) 751-756. | MR 903515 | Zbl 0604.90098

[12] R.T. Rockafellar, "Local boundedness of nonlinear, monotone operators," Michigan Mathematical Journal 16 (1969) 397-407. | MR 253014 | Zbl 0175.45002

[13] R.T. Rockafellar, Convex Analysis (Princeton University Press, Princeton, NJ, 1970). | MR 274683 | Zbl 0193.18401

[14] J. -J. Strodiot, V.H. Nguyen, and N. Heukemes, "∈- optimal solutions in nondifferentiable programming and some related questions," Math. Programming 25 (1983) 307-328. | MR 689660 | Zbl 0495.90067