Journal of Optimization Theory and Applications

, Volume 141, Issue 3, pp 597–618

Convergent Bounds for Stochastic Programs with Expected Value Constraints


DOI: 10.1007/s10957-008-9476-1

Cite this article as:
Kuhn, D. J Optim Theory Appl (2009) 141: 597. doi:10.1007/s10957-008-9476-1


This article describes a bounding approximation scheme for convex multistage stochastic programs (MSP) that constrain the conditional expectation of some decision-dependent random variables. Expected value constraints of this type are useful for modelling a decision maker’s risk preferences, but they may also arise as artifacts of stage-aggregation. We develop two finite-dimensional approximate problems that provide bounds on the (infinite-dimensional) original problem, and we show that the gap between the bounds can be made smaller than any prescribed tolerance. Moreover, the solutions of the approximate MSPs give rise to a feasible policy for the original MSP, and this policy’s optimality gap is shown to be smaller than the difference of the bounds. The considered problem class comprises models with integrated chance constraints and conditional value-at-risk constraints. No relatively complete recourse is assumed.


Stochastic programming Approximation Bounds Expected value constraints Integrated chance constraints 

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of ComputingImperial College of Science, Technology, and MedicineLondonUK

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