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Convergent Bounds for Stochastic Programs with Expected Value Constraints

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abstract 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.
   
type journal paper
   
keywords Stochastic programming, Approximation, Bounds, Expected value constraints, Integrated chance constraints
   
language English
kind of paper journal article
date of appearance 1-6-2009
journal Journal of Optimization Theory and Applications
publisher Springer Netherlands
ISSN 0022-3239
ISSN (online) 1573-2878
volume of journal 141
number of issue 3
page(s) 597-618
review double-blind review
   
citation Kuhn, D. (2009). Convergent Bounds for Stochastic Programs with Expected Value Constraints. Journal of Optimization Theory and Applications, 141(3), 597-618.