Accessible to a variety of readers, this book is of interest to
specialists, graduate students and researchers in mathematics,
optimization, computer science, operations research, management science,
engineering and other applied areas interested in solving optimization
problems. Basic principles, potential and boundaries of applicability of
stochastic global optimization techniques are examined in this book. A
variety of issues that face specialists in global optimization are
explored, such as multidimensional spaces which are frequently ignored
by researchers. The importance of precise interpretation of the
mathematical results in assessments of optimization methods is
demonstrated through examples of convergence in probability of random
search. Methodological issues concerning construction and applicability
of stochastic global optimization methods are discussed, including the
one-step optimal average improvement method based on a statistical model
of the objective function. A significant portion of this book is devoted
to an analysis of high-dimensional global optimization problems and the
so-called 'curse of dimensionality'. An examination of the three
different classes of high-dimensional optimization problems, the
geometry of high-dimensional balls and cubes, very slow convergence of
global random search algorithms in large-dimensional problems, and poor
uniformity of the uniformly distributed sequences of points are included
in this book.
