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Book review

Author(s) Floudas, C.A. (ed.)
Pardalos, P.M. (ed.)
Title Recent advances in global optimization
Publisher Princeton University Press
Year of publication 1992
Reviewed by Anatoly Zhigljavsky

The volume contains 27 works concerning different kinds of optimization problems. Surprisingly, the first 7 works have no relation to the global optimization declared in the title. These articles and a few others concern problems of quadratic, linear and integer programming. The level of the articles is reasonably high, one can see some very well known names, specifically N. Karmarkar and S. Vavasis, among their authors.

Excluding the mentioned articles and some simple ones on applications, one can find about a half of the volume, 13 articles by my count, which correspond to the title and indeed reflect some recent advances in global optimization. The average level of the articles on global optimization is also quite high. However, I do not agree with the editors declared that "this book highlights a wide spectrum of creativity and richness of ideas ... of global optimization". My claim is that most of the articles concern only particular problems, I have found merely a small part of ideas of global optimization in the volume. For example, the methods based on stochastic and axiomatic models of the objective function are only mentioned in the book. Furthermore, a huge area of global random search was out of consideration.

A natural competitor for the volume is the "Journal of Global Optimization". For those interested in global optimization as a subject I do also recommend the following monographs: R. Horst, H. Tuy, Global optimization (deterministic approaches), Springer-Verlag, 1990; A. Torn, A. Zilinskas, Global optimization, Springer-Verlag, 1989; and A. Zhigljavsky, Theory of global random search, Kluwer Academic Publishers, 1991.

Generally, the volume is of reasonably good production quality and contains a lot of interesting articles in the fields of global optimization as well as quadratic, linear and integer programming. Correspondingly, it may be of interest for many specialists in optimization. Purchase of the volume might be a good investment for such specialists as well as the libraries of the institutions which have optimization as one of the fields of their research.