Partition-based distributionally robust optimization via optimal transport with order cone constraints

Abstract In this paper we wish to tackle stochastic programs affected by ambiguity about the probability law that governs their uncertain parameters. Using optimal transport theory, construct an set exploits knowledge distribution of parameters, which is provided by: (1) sample data and (2) a-priori information on order among probabilities true data-generating assigns some regions its support set. This type enforced means cone constraints can encode a wide range shape parameters such as related monotonicity or multi-modality. We seek decisions are distributionally robust. number practical cases, resulting robust optimization (DRO) problem be reformulated finite convex where translates into linear constraints. addition, our method inherits finite-sample performance guarantees Wasserstein-metric-based DRO approach proposed Mohajerin Esfahani Kuhn (Math Program 171(1–2):115–166. https://doi.org/10.1007/s10107-017-1172-1 , 2018), while generalizing other popular approaches. Finally, have designed numerical experiments analyze with newsvendor strategic firm competing à la Cournot in market.