Advances in Polynomial Optimization

  1. González Rodríguez, Brais
Dirixida por:
  1. Julio González Díaz Director
  2. Beatriz Pateiro López Director

Universidade de defensa: Universidade de Santiago de Compostela

Fecha de defensa: 02 de decembro de 2022

Tribunal:
  1. Emilio Carrizosa Priego Presidente/a
  2. Balbina Virginia Casas Méndez Secretaria
  3. Marcos Raydan Vogal
Departamento:
  1. Departamento de Estatística, Análise Matemática e Optimización

Tipo: Tese

Teseo: 764033 DIALNET

Resumo

Polynomial 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.