Preliminaries

Abstract

The main purpose of this book is to introduce techniques and software for the verified solution of nonlinear systems of equations and for rigorous, deterministic unconstrained and constrained global optimization. Specifically, global optima or solutions of nonlinear equations will be sought within the box

$$ X = \left\{ {{{({x_1},{x_2},...,{x_n})}^T} \in {R^n}/{{\underline x }_i} \le {x_i} \le \overline {{x_i}} ,1 \le i \le n} \right\}$$

((1.1))

for some set of lower bounds $\left\{ {{{\underline x }_i}} \right\}_i^n = 1$ and upper bounds $\left\{ {{{\overline x }_i}} \right\}_i^n = 1$.