From CVaR to uncertainty set: Implications in joint chance-constrained optimization

From CVaR to uncertainty set: Implications in joint chance-constrained optimization

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Article ID: iaor20104027
Volume: 58
Issue: 2
Start Page Number: 470
End Page Number: 485
Publication Date: Mar 2010
Journal: Operations Research
Authors: , , ,
Keywords: chance-constrained optimisation, value at risk
Abstract:

We review and develop different tractable approximations to individual chance-constrained problems in robust optimization on a variety of uncertainty sets and show their interesting connections with bounds on the conditional-value-at-risk (CVaR) measure. We extend the idea to joint chance-constrained problems and provide a new formulation that improves upon the standard approach. Our approach builds on a classical worst-case bound for order statistics problems and is applicable even if the constraints are correlated. We provide an application of the model on a network resource allocation problem with uncertain demand.

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