Ambiguous Joint Chance Constraints Under Mean and Dispersion Information

We study joint chance constraints where the distribution of the uncertain parameters is onlyknown to belong to an ambiguity set characterized by the mean and support of the uncertaintiesand by an upper bound on their dispersion. This setting gives rise to pessimistic (optimistic)ambiguous chance constraints, which require the corresponding classical chance constraints to besatisfied for every (for at least one) distribution in the ambiguity set. We demonstrate that thepessimistic joint chance constraints are conic representable and thus computationally tractableif (i) the constraint coefficients of the decisions are deterministic, (ii) the support set of theuncertain parameters is a cone, and (iii) their dispersion function is positively homogeneous.We also show that tractability is lost as soon as either of the conditions (i), (ii) or (iii) is relaxedin the mildest possible way. We further prove that the optimistic joint chance constraints aretractable if and only if (i) holds. To showcase the power of our tractability results, we solvelarge-scale project management and image reconstruction models to global optimality.