RT Dissertation/Thesis
T1 Theory and applications of Distributionally Robust Optimization with side data
A1 Esteban-Pérez, Adrián
K1 Optimización matemática - Tesis doctorales
AB Nowadays, a large amount of varied data is being generated which, when made availableto the decision maker, constitutes a valuable resource in optimization problems.These data, however, are not free from uncertainty about the physical, economic orsocial context, system or process from which they originate; uncertainty that, on theother 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 andinvestigate methods for solving optimization problems where there is a great diversityof data on uncertain phenomena. Today’s decision makers not only collect observationsfrom the uncertainties directly affecting their decision-making processes, but also gathersome prior information about the data-generating distribution of the uncertainty. Thisinformation is used by the decision maker to prescribe a more accurate set of potentialprobability distributions, the so-called ambiguity set in distributionally robust optimization.Our intention, therefore, is to develop a purely data-driven methodology, withinthe scope of distributionally robust optimization based on the optimal transportationproblem, 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 probabilitydistribution; second, some conditional information such as that given by various covariates,which help explain the random phenomenon underlying the optimization problemwithout resorting to prior regression techniques.
PB UMA Editorial
YR 2022
FD 2022
LK https://hdl.handle.net/10630/25410
UL https://hdl.handle.net/10630/25410
LA eng
NO We propose a formulation of a distributionally robust approach to model certainstructural information about the probability distribution of the uncertainty. This isgiven in terms of a partition-based approach, exploiting the optimal transport problemand order cone constraints. In addition, tractable reformulations are provided, andby the same token, the power of modeling shape information (such as multimodality),without jeopardizing the complexity of the distributionally robust optimization problemby adding linear constraints.Moreover, by leveraging probability trimmings and their connection with the partialoptimal transport problem, we formulate a distributionally robust version of conditionalstochastic programs. The theoretical performance guarantees of the distributionally robust frameworks we propose are also formally stated and discussed. In addition, weshow that the proposed methodology based on probability trimmings can be applied todecision-making problems under uncertainty with contaminated samples.Furthermore, we develop a distributionally robust chance-constrained Optimal PowerFlow model that is able to exploit contextual/side information through an ambiguityset based on probability trimmings, providing a tractable reformulation using the well-knownconditional value-at-risk approximation.Finally, we test, analyze, and discuss the proposed optimization models and methodologiesdeveloped in this PhD dissertation through illustrative examples and realisticcase studies in finance, inventory management and power systems operation.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 19 ene 2026