From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization

We review and develop different tractable approximations to individual chance constrained problems in robust optimization on a varieties 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 problem 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