2026-05-30T07:02:38Zhttps://riuma.uma.es/rest/oai/request

oai:riuma.uma.es:10630/254102026-02-03T12:42:58Zcom_10630_2254col_10630_37957

Theory and applications of Distributionally Robust Optimization with side data Esteban-Pérez, Adrián Morales-González, Juan Miguel Optimización matemática - Tesis doctorales We propose a formulation of a distributionally robust approach to model certain structural information about the probability distribution of the uncertainty. This is given in terms of a partition-based approach, exploiting the optimal transport problem and order cone constraints. In addition, tractable reformulations are provided, and by the same token, the power of modeling shape information (such as multimodality), without jeopardizing the complexity of the distributionally robust optimization problem by adding linear constraints. Moreover, by leveraging probability trimmings and their connection with the partial optimal transport problem, we formulate a distributionally robust version of conditional stochastic programs. The theoretical performance guarantees of the distributionally robust frameworks we propose are also formally stated and discussed. In addition, we show that the proposed methodology based on probability trimmings can be applied to decision-making problems under uncertainty with contaminated samples. Furthermore, we develop a distributionally robust chance-constrained Optimal Power Flow model that is able to exploit contextual/side information through an ambiguity set based on probability trimmings, providing a tractable reformulation using the well-known conditional value-at-risk approximation. Finally, we test, analyze, and discuss the proposed optimization models and methodologies developed in this PhD dissertation through illustrative examples and realistic case studies in finance, inventory management and power systems operation. Nowadays, a large amount of varied data is being generated which, when made available to the decision maker, constitutes a valuable resource in optimization problems. These data, however, are not free from uncertainty about the physical, economic or social context, system or process from which they originate; uncertainty that, on the other hand, the decision maker must take into account in his/her decision making process. The objective of this PhD dissertation is to develop theoretical foundations and investigate methods for solving optimization problems where there is a great diversity of data on uncertain phenomena. Today’s decision makers not only collect observations from the uncertainties directly affecting their decision-making processes, but also gather some prior information about the data-generating distribution of the uncertainty. This information is used by the decision maker to prescribe a more accurate set of potential probability distributions, the so-called ambiguity set in distributionally robust optimization. Our intention, therefore, is to develop a purely data-driven methodology, within the scope of distributionally robust optimization based on the optimal transportation problem, which exploits some extra/prior information about the random phenomenon. This extra information crystallizes in two axes on the nature of the random phenomenon: first, some prior information about, for example, the shape/structure of the probability distribution; second, some conditional information such as that given by various covariates, which help explain the random phenomenon underlying the optimization problem without resorting to prior regression techniques. 2022-11-11T12:22:23Z 2022-11-11T12:22:23Z 2022-07-27 2022 2022-09-27 doctoral thesis https://hdl.handle.net/10630/25410 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional UMA Editorial