Bundle-based decomposition : conditions for convergence

S. M. Robinson

Annales de l'I.H.P. Analyse non linéaire (1989)

  • Volume: S6, page 435-447
  • ISSN: 0294-1449

How to cite


Robinson, S. M.. "Bundle-based decomposition : conditions for convergence." Annales de l'I.H.P. Analyse non linéaire S6 (1989): 435-447. <http://eudml.org/doc/78206>.

author = {Robinson, S. M.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Bundle-based decomposition; decentralized convex optimization; Computational tests; approximate minimization},
language = {eng},
pages = {435-447},
publisher = {Gauthier-Villars},
title = {Bundle-based decomposition : conditions for convergence},
url = {http://eudml.org/doc/78206},
volume = {S6},
year = {1989},

AU - Robinson, S. M.
TI - Bundle-based decomposition : conditions for convergence
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1989
PB - Gauthier-Villars
VL - S6
SP - 435
EP - 447
LA - eng
KW - Bundle-based decomposition; decentralized convex optimization; Computational tests; approximate minimization
UR - http://eudml.org/doc/78206
ER -


  1. [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). Zbl0252.47055MR348562
  2. [2] H. Brézis and A. Haraux, "Image d'une somme d'opérateurs monotones et applications," Israel Journal of Mathematics23 (1976) 165-186. Zbl0323.47041MR399965
  3. [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. Zbl0539.90063MR612625
  4. [4] J.K. Ho and E. Loute, "DECOMP User's Guide," unpublished manuscript. 
  5. [5] T. Kato, "Demicontinuity, hemicontinuity, and monotonicity," Bull. Amer. Math. Soc.70 (1964) 548-550. Zbl0123.10701MR163198
  6. [6] T. Kato, "Demicontinuity, hemicontinuity, and monotonicity. II," Bull. Amer. Math. Soc.73 (1967) 886-889. Zbl0184.36504MR238135
  7. [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 Programming4 (Academic Press, New York, 1981) 245-282. Zbl0533.49023MR663383
  8. [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. Zbl0468.90063MR628449
  9. [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. [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. [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. Zbl0604.90098MR903515
  12. [12] R.T. Rockafellar, "Local boundedness of nonlinear, monotone operators," Michigan Mathematical Journal16 (1969) 397-407. Zbl0175.45002MR253014
  13. [13] R.T. Rockafellar, Convex Analysis (Princeton University Press, Princeton, NJ, 1970). Zbl0193.18401MR274683
  14. [14] J. -J. Strodiot, V.H. Nguyen, and N. Heukemes, "∈- optimal solutions in nondifferentiable programming and some related questions," Math. Programming25 (1983) 307-328. Zbl0495.90067MR689660

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