Polynomial optimisation

Abstract

This series of lectures will introduce polynomial optimisation and decision problems, what they can model, how they can be attacked using tools from convex optimisation. The lectures will be illustrated, throughout, with a range of concrete applications. These lectures are designed to be accessible to novices to the field who have a mathematics and computational background, such as phd students, postdoc and/or inquisitive academics who wish to have a better understanding of recent advances in this dynamic field. 

Optimisation and decision problems where the objective function and the constraints can be formulated using multivariate polynomials can model a very wide range of problems from areas as diverse as dynamical systems and control, probability and statistics, quantum information, and combinatorial optimisation. Such problems, while very expressive, are generally difficult to solve. Despite this, systematic and powerful methods based on tools from convex optimisation and convex geometry have been developed to globally approximate these challenging problems.