Abstract
Information structure is introduced as a decision variable in two-stage stochastic programming. To this end the notion of sensors is employed. The outcome resembles a three-stage stochastic program, and hence can be analyzed with standard tools. This is demonstrated by establishing a strong law of large numbers for the two-stage problem with the information variable.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Artstein, Z. and Wets, R. J-B (1993). Sensors and information in optimization under stochastic uncertainty. Math. Oper. Res. 18, 523–547.
Artstein, Z. and Wets, R. J-B (1993)a. Stability results for stochastic programs and sensors, allowing for discontinuous objective functions. Preprint, to appear in SIAM J. Optimization.
Attouch, H. and Wets, R. J-B (1991). Epigraphical processes: laws of large numbers for random lsc functions. Preprint, University of California, Davis.
Beer, G. (1987). A geometric algorithm for approximating semi continuous functions. J. Approx. Theory 49, 31–40.
Billingsley, P. (1968). Convergence of Probability Measures. John Wiley, New York.
Bourbaki, N. (1959). Integration, Chapitre 6. Herman, Paris.
DeGroot, M.H. (1970). Optimal Statistical Decisions. McGraw-Hill, New York.
Dupaunnvá, J. (1991). On statistical sensitivity analysis in stochastic programming. Ann. of Oper. Res. 30, 199–214.
King, A.J. and Wets, R. J-B (1991). Epi-consistency of convex stochastic programs. Stochastics and Stochastics Reports 34, 83–92.
Neveu, J. (1965). Mathematical Foundation of the Calculus of Probability. Holden Day, San Francisco.
Robinson, S.M. and Wets, R. J-B (1987). Stability in two stage stochastic programming. SIAM J. Control and Opt. 25, 1409–1416.
Rockafellar, R.T. and Wets, R. J-B (1984). Variational analysis: an introduction. In Multifunction and Integrands, Stochastic Analysis and Optimization, G. Salinetti, ed., Lecture Notes in Mathematics 1091, Springer-Verlag, Berlin, pp. 1–54.
Römisch, W. and Schultz, R. (1991). Stability analysis for stochastic programs. Ann. of Oper. Res. 30, 241–266.
Schultz, R. (1992). Continuity and stabilization in two-stage stochastic integer programming. In Stochastic Optimization, Numerical Methods and Technical Applications, K. Marti, ed., Lecture Notes in Economics and Mathematical Systems 379, Springer-Verlag, Berlin, pp. 81–92.
Schultz, R. (1992). Continuity properties of the expectation functions in stochastic integer programming. Math, of Oper. Res. 18, 578–589.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Artstein, Z. (1994). Probing for Information in Two-Stage Stochastic Programming and the Associated Consistency. In: Mandl, P., Hušková, M. (eds) Asymptotic Statistics. Contributions to Statistics. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57984-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-57984-4_2
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-0770-7
Online ISBN: 978-3-642-57984-4
eBook Packages: Springer Book Archive