Globalized distributionally robust optimization based on samples

A set of perturbed data is key to robust optimization modelling. Distributionally robust optimization (DRO) is a methodology used for optimization problems affected by random parameters with an uncertain probability distribution. In terms of the perturbed data, it is essential to estimate an appropriate support set for the probability distribution when formulating DRO models. In this study, we introduce two globalized distributionally robust optimization (GDRO) models that choose a core set based on data and a sample space containing the core set to balance the degree of robustness and conservatism simultaneously. The degree of conservatism can be controlled by the expected distance of random parameters from the core set. Under certain assumptions, we reformulate several GDRO models into tractable semi-definite programs. In addition, numerical experiments were conducted to demonstrate the performance of the GDRO approach and the relationship between the optimal objective values of the GDRO models and the size of the sample space and the core set.