Contributions to the design of polynomial optimization algorithms

Abstract

In the effort of developing algorithms for solving nonlinear optimization problems, most of the research is aimed at solving general nonlinear problems. However, there is a subclass of problems, polynomial optimization problems, that it’s relevant as it provides an additional structure to the problems while still covering classes of problems often studied, such as continuous convex and nonconvex problems with quadratic costs and constraints or binary linear problems. In this thesis, we study this field of polynomial optimization and focus on three relevant aspects: solving the problem, using learning techniques to improve the performance of a solver and applying polynomial optimization techniques to a real-world problem in power network optimization.