Rosa, Charles H.; Takriti, Samer Improving aggregation bounds for two-stage stochastic programs. (English) Zbl 0955.90097 Oper. Res. Lett. 24, No. 3, 127-137 (1999). Summary: Stochastic multi-stage linear programs are rarely used in practical applications due to their size and complexity. Using a general matrix to aggregate the constraints of the deterministic equivalent yields a lower bound. A similar aggregation in the dual space provides an upper bound on the optimal value of the given stochastic program. Jensen’s inequality and other approximations based on aggregation are a special case of the suggested approach. The lower and upper bounds are tightened by updating the aggregating weights. Cited in 8 Documents MSC: 90C15 Stochastic programming Keywords:aggregation bounds; two-stage stochastic programs; lower bound; upper bound; Jensen’s inequality Software:AMPL; OSL; MSLiP PDFBibTeX XMLCite \textit{C. H. Rosa} and \textit{S. Takriti}, Oper. Res. Lett. 24, No. 3, 127--137 (1999; Zbl 0955.90097) Full Text: DOI References: [2] Birge, J. R., Aggregation bounds in stochastic linear programming, Math. Programm., 31, 25-41 (1985) · Zbl 0562.90066 [3] Birge, J. R.; Takriti, S., Successive approximation of linear control models, SIAM J. Control Optim., 37, 1, 165-176 (1998) · Zbl 0916.90212 [4] Birge, J. R.; Wets, R. J.-B., Sublinear upper bounds for stochastic programs with recourse, Math. Programm., 43, 131-149 (1989) · Zbl 0663.90063 [6] Gassmann, H., MSLIP: a computer code for the multistage stochastic linear programming problem, Math. Programm., 47, 407-423 (1990) · Zbl 0701.90070 [8] Huberman, G., Error bounds for the aggregated convex programming problem, Math. Programm., 26, 100-108 (1983) · Zbl 0516.90060 [12] Wright, S. E., Primal-dual aggregation and disaggregation for stochastic linear programs, Math. Oper. Res, 19, 4, 893-908 (1994) · Zbl 0821.90086 [13] Zipkin, P. H., Bounds for row-aggregation in linear programming, Oper. Res, 28, 4, 903-916 (1980) · Zbl 0441.90057 [14] Zipkin, P. H., Bounds on the effect of aggregating variables in linear programs, Oper. Res., 28, 2, 403-418 (1980) · Zbl 0426.90056 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.