Advances in Polynomial Optimization

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.