A Sensitivity Method for Solving Multistage Stochastic Linear Programming Problems
A version of the simplex method for solving stochastic linear control problems is presented. The method takes advantage of the structure of the problem to achieve utmost memory economy in both data representation and basis inverse management.
KeywordsSimplex Method Sensitivity Matrix Multistage Stochastic Program Basis Inverse General Sparse Matrix
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- Daniel, J. W., Gragg, W. B., Kaufman, L. and Stewart, G. W. (1976). Reorthogonalization and stable algorithms for updating the Gram—Schmidt QR factorization. Mathematics of Computation 30, pp. 772–795.Google Scholar
- Gondzio, J. (1988a). Stable variant of the simplex method for solving supersparse linear programs. 3rd International Symposium on Systems Analysis and Simulation, Berlin 1988.Google Scholar
- Gondzio, J. (1988b). Simplex modifications exploiting special features of dynamic and stochastic dynamic linear programming problems. Control and Cybernetics, 1988 (to appear).Google Scholar
- Gondzio, J. and Ruszczynski, A. (1986). A package for solving dynamic linear programs. Institute of Automatic Control, Warsaw University of Technology, 1986 (in Polish).Google Scholar
- Murtagh, B. (1981). Advanced Linear Programming. McGraw—Hill, 1981.Google Scholar
- Murtagh, B. and Saunders, M. (1983). MINOS 5.0. User’s guide. System Optimization Laboratory, Stanford University, 1983.Google Scholar
- Perold, A. F. and Dantzig, G. B. (1979). A basis factorization method for block triangular linear programs. in: Duff, I. S. and Stewart G. W. eds., Sparse Matrix Proceedings 1978, SIAM, Philadelphia, pp. 283–312.Google Scholar
- Wets, R. J.—B. (1986). Large scale linear programming techniques in stochastic programming. in: Ermoliev, Y. and Wets R. J.—B. (eds), Numerical Methods in Stochastic Programming, Springer—Verlag, Berlin 1986.Google Scholar