Introduction

This book is about guaranteed numerical methods for approximating sets, and their application to engineering. Guaranteed means here that outer (and sometimes inner) approximations of the sets of interest are obtained, which can, at least in principle, be made as precise as desired. It thus becomes possible to achieve tasks often thought to be out of the reach of numerical methods, such as finding all solutions of sets of non-linear equations and inequalities or all global optimizers of possibly multi-modal criteria.