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Nested decomposition of multistage nonlinear programs with recourse.(English)Zbl 0619.90054

Authors’ abstract: ”Nested decomposition is extended to the case of arborescent nonlinear programs. Duals of extensive forms of nonlinear multistage stochastic programs constitute a particular class of those problems; the method is tested on a set of problems of that type.”
Reviewer: W.-R.Heilmann

MSC:

90C15 Stochastic programming
90C30 Nonlinear programming

Software:

MINOS;LIFT

Cite

References:

[1]D. Ament, J.K. Ho, E. Loute and M. Remmelswaal, ”LIFT: A nested decomposition algorithm for solving lower block triangular linear programs,” in: G.B. Dantzig, M.A.H. Dempster and M.J. Kallio, eds.,Large Scale Programming (IIASA, Laxenburg, 1981) pp. 383–408. ·Zbl 0538.90053
[2]J.F. Benders, ”Partitioning procedures for solving mixed variables programming problems,”Numerische Mathematik 1 (1982) 238–252. ·Zbl 0109.38302
[3]J.R. Birge, ”Decomposition and partitioning methods for multi-stage stochastic linear programs,”Operations Research 33 (1985) 989–1007. ·Zbl 0581.90065 ·doi:10.1287/opre.33.5.989
[4]G.B. Dantzig and A. Madansky, ”On the solution of two-stage linear programs under uncertainty,” in:Proceedings, 4th Berkeley Symposium on Mathematical Statistics and Probability (UC Press, Berkeley, 1961). ·Zbl 0104.14401
[5]G.B. Dantzig and P. Wolfe, ”The decomposition principle for linear programs,”Operations Research 8 (1960) 101–111. ·Zbl 0093.32806 ·doi:10.1287/opre.8.1.101
[6]G.B. Dantzig,Linear Programming and Extensions (Princeton University Press, Princeton, 1963).
[7]X. de Groote, M.-C. Noël and Y. Smeers, ”Some test problems for stochastic nonlinear multistage programs,” to appear in: Y. Ermoliev and R. Wets, eds.,Numerical Techniques for Stochastic Optimization Problems (IIASA, Laxenburg, 1986). ·Zbl 0677.90048
[8]J.K. Ho and A.S. Manne, ”Nested decomposition for dynamic models,”Mathematical Programming 6 (1974) 121–140. ·Zbl 0294.90051 ·doi:10.1007/BF01580231
[9]J.K. Ho, Nested decomposition of large scale linear programs with the staircase structure,” Ph.D. Dissertation, Stanford University (Stanford, 1974).
[10]J.K. Ho and E. Loute, ”Computational experience with advanced implementation of decomposition algorithms for linear programming”,Mathematical Programming 27 (1983) 283–290. ·Zbl 0521.65043 ·doi:10.1007/BF02591904
[11]M. Kallio and E.L. Porteus, ”Decomposition of arborescent linear programs,”Mathematical Programming 13(1977) 348–356. ·Zbl 0377.90068 ·doi:10.1007/BF01584347
[12]A.S. Manne, ”ETA-MACRO: A model of energy-economy interactions,” Research Project 1014, Department of Operations Research, Stanford University, Stanford, California 94305 (1977).
[13]A.S. Manne, M.A. Beltramo, T.F. Rutherford, A.N. Svoronos and T.F. Wilson, ”ETA-MACRO: A progress report,” Research Project 1014, Department of Operations Research, Stanford University, Stanford, California 94305 (1983).
[14]A.B. Murtagh and M.A. Saunders, ”Minos: A large-scale nonlinear programming system,” User’s guide. Technical Report 77-9, Stanford University, Department of Operations Research (1977).
[15]M.-C. Noël and Y. Smeers, ”On the use of nested decomposition for solving non-linear multistage stochastic programs,” in: F. Archetti, D. Di Pillo and M. Lucertini, eds.,Stochastic Programming (Springer-Verlag, Berlin, 1985) pp. 235–245.
[16]P. Olsen, ”Multistage stochastic programming with recourse: the equivalent deterministic problem,”SIAM Journal on Control and Optimization 14 (876) 495–517. ·Zbl 0336.90039
[17]R.P. O’Neill, ”Nested decomposition of multistage convex programs,”SIAM Journal on Control and Optimization 14 (1976) 409–418. ·Zbl 0333.90039 ·doi:10.1137/0314027
[18]R.T. Rockafellar,Convex Analysis (Princeton University Press, Princeton, 1970). ·Zbl 0193.18401
[19]R.M. Van Slyke and R. Wets, ”L-shaped linear programs with applications to optimal control and stochastic programming,”SIAM Journal on Applied Mathematics 17 (1969) 638–663. ·Zbl 0197.45602 ·doi:10.1137/0117061
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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