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 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