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Book review

Author(s) Pervozvanskii, A.A.
Gaitsgori, V.G.
Title Theory of suboptimal decisions
Publisher Kluwer
Year of publication 1988
Reviewed by Frantisek Vcelar

The book treats approximate solving of optimization problems. The method under discussion consists of perturbation combined with aggregation and decomposition. This setup is quite helpful in many cases when some structural complexity has to be overcome. One can then obtain a relatively good solutions both for optimal control and for decision making problems. This applies, in particular, to the situations where standard methods fail or prove too expensive. The point is to perform a slight change (perturbation) to the problem under consideration, so as to obtain a similar problem which is easier to solve.

The exposition in the book is clear and precise, and is divided into six chapters. The general philosophy of the method is outlined in the introduction, results on perturbations follow in the first chapter, and the remaining chapters discuss some special cases and applications.

The authors have brought together a handsome collection of material from this field of research. By the very nature of the subject, any reading requires, of course, certain knowledge of the optimization theory and matrix algebra. Consequently, the book is addressed to specialists in optimization theory, mathematical economics, and control theory. To such researchers, purchasing the book will represent a worthwhile contribution to their personal library. Besides, the book could also be helpful as a textbook for special courses and graduate students.