Convergent Bounds for Stochastic Programs with Expected Value Constraints
Journal
Journal of Optimization Theory and Applications
ISSN
1573-2878
ISSN-Digital
0022-3239
Type
journal article
Date Issued
2009-06-01
Author(s)
Kuhn, Daniel
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.
Language
English
Keywords
Stochastic programming
Approximation
Bounds
Expected value constraints
Integrated chance constraints
HSG Classification
contribution to scientific community
Refereed
Yes
Publisher
Springer Science + Business Media
Publisher place
Dordrecht
Volume
141
Number
3
Start page
597
End page
618
Pages
22
Subject(s)
Division(s)
Eprints ID
60650