The vast majority of important applications in science, engineering and
applied science are characterized by the existence of multiple minima
and maxima, as well as first, second and higher order saddle points. The
area of Deterministic Global Optimization introduces theoretical,
algorithmic and computational ad- vances that (i) address the
computation and characterization of global minima and maxima, (ii)
determine valid lower and upper bounds on the global minima and maxima,
and (iii) address the enclosure of all solutions of nonlinear con-
strained systems of equations. Global optimization applications are
widespread in all disciplines and they range from atomistic or molecular
level to process and product level representations. The primary goal of
this book is three fold: first, to introduce the reader to the basics of
deterministic global optimization; second, to present important
theoretical and algorithmic advances for several classes of mathematical
prob- lems that include biconvex and bilinear; problems, signomial
problems, general twice differentiable nonlinear problems, mixed integer
nonlinear problems, and the enclosure of all solutions of nonlinear
constrained systems of equations; and third, to tie the theory and
methods together with a variety of important applications.