## Algorithms for Minimization without Derivatives

## Preface to the Dover edition

Since the first edition of
*Algorithms for Minimization without Derivatives*
was published in 1973, there has been a great deal
of research on algorithms for optimization of functions of several variables,
the topic of Chapter 7.
Also, techniques for computing derivatives analytically
have been refined by my former student
Andreas Griewank and others, so there
is now less reason to consider algorithms which use only function values.
Despite this progress, much of the book is still relevant. The old and
deceptively simple problem of approximating a zero of a function of one
variable has not gone away. It often occurs as a component of a larger problem,
so the efficiency of the algorithm used is important. For example, in their
disproof of the Mertens conjecture,
Odlyzko and
te Riele
needed highly accurate values of 2,000
zeros
of the Riemann zeta function. Thus, Chapters 3
and are still useful.

Similarly, the problems of approximating local minima of functions of one
variable, or global minima of functions of a small number of variables,
are still with us, and the algorithms of
Chapters 5 and 6 are still relevant.

When Dover
offered to reprint the book, which had been out of print for
many years, I was happy to accept. My first impulse was to start from the
beginning and rewrite the book, incorporating the most important advances
made in the past thirty years, but this impulse was discarded when I realised
the scale of the undertaking. With the aim of producing the Dover edition
as quickly as possible, a decision was made to reprint the first edition
"warts and all", and to maintain a web site at which corrections, updates,
programs, and additional references could be found. The web site is at
http://www.comlab.ox.ac.uk/oucl/work/richard.brent
and readers are invited to visit it.

I would like to thank my mentor and former thesis advisor
Gene Golub
for putting me in contact with Dover, and John Grafton of Dover for his
advice on several matters related to the production of the Dover edition.
Finally, I take the opportunity to thank again all those (unfortunately
not all still living) who contributed in various ways to the first edition.

R. P. Brent

Oxford, February 2001