González Díaz, JulioPateiro López, BeatrizGonzález Rodríguez, Brais2023-01-182023-01-182022http://hdl.handle.net/10347/29918Polynomial optimization has a wide range of practical applications in fields such as optimal control, energy and water networks, facility location, management science, and finance. It also generalizes relevant optimization problems thoroughly studied in the literature, such as mixed-binary linear optimization, quadratic optimization, and complementarity problems. As finding globally optimal solutions is an extremely challenging task, the development of efficient techniques for solving polynomial optimization problems is of particular relevance. In this thesis we provide a detailed study of different techniques to solve this kind of problems and we introduce some nobel approaches in this field, including the use of statistical learning techniques. Furthermore, we also present a practical application of polynomial optimization to finance and more specifically, portfolio design.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Polynomial optimizationReformulation-Linearization TechniqueAlgorithmBranch and boundMachine learningStatistical learningConic optimizationPortfolio designMaterias::Investigación::12 Matemáticas::1207 Investigación operativa::120711 Programación no linealMaterias::Investigación::12 Matemáticas::1207 Investigación operativa::120709 Programación linealMaterias::Investigación::12 Matemáticas::1209 Estadística::120903 Análisis de datosdoctoral thesisopen access