Abstract
Most systems that need to be controlled or analyzed involve some level of uncertainty about the value to assign to some of the parameters, if not about the actual layout of certain subcomponents of the system. In many situations not much is lost by assigning “reasonable” values to these parameters or by choosing a particular design. In other instances ignoring uncertainty may very well lead to totally misleading solutions that would invalidate any of the implications one may wish to draw from the analysis.
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References
Back, Kerry and Stanley Pliska, “The shadow price of information in continuous time decision problems”, Stochastics 22(1987), 151–168.
Dempster, Michael, “On stochastic programming: II, Dynamic problems under risk”, Research Report DAL TR 86-5, Dalhousie University, July 1985 (revised June 1986).
Evstigneev, Igor V., “Prices on information and stochastic insurance models”, IIASA CP-85-23 (Laxenburg), April 1985.
Mulvey, John and Hercules Vladimirou, Solving multistage investment problems: an application of scenario aggregation, Statistics and Operations Research SOR 88-1, Princeton University, 1988. Mulvey, John and Hercules Vladimirou, Solving multistage stochastic networks: an application of scenario aggregation, Statistics and Operations Report SOR 88-2, Princeton University, 1988.
Robinson, Stephen M. and Roger J-B Wets, “Stability in two-stage stochastic programming”, SIAM J. on Control and Optimization 25(1987), 1409–1416.
Rockafellar, R.T. and Roger J-B Wets, “Stochastic Convex Programming: Kuhn-Tucker Conditions”, J. Mathematical Economics 2(1975), 349–370.
Rockafellar, R.T. and Roger J-B Wets, “Nonanticipativity and ℒ1-Martingales in Stochastic Optimization Problems”, Mathematical Programming Study 6(1976), 170–187. Also in: Stochastic Systems: Modeling, Identification and Optimization, R. Wets (ed.), North-Holland, Amsterdam, 1976.
Rockafellar, R.T. and Roger J-B Wets, “Scenario and policy aggregation in optimization under uncertainty”, IIASA Working Paper WP-87-119, Laxenburg, Austria, December 1987.
Wets, Roger J-B, Large-scale linear programming techniques in stochastic programming, in Numerical Methods for Stochastic Optimization, eds. Y. Ermoliev and R. Wets, Springer Verlag, Berlin, 1987.
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© 1989 Springer-Verlag Berlin Heidelberg
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Wets, R.JB. (1989). The Aggregation Principle in Scenario Analysis and Stochastic Optimization. In: Wallace, S.W. (eds) Algorithms and Model Formulations in Mathematical Programming. NATO ASI Series, vol 51. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83724-1_4
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DOI: https://doi.org/10.1007/978-3-642-83724-1_4
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