Entropy optimization principles with applications / J. N. Kapur, H. K. Kesavan

This book aims to be a textbook or handbook for graduate studies on the types of problems which can be solved by using the maximum entropy principle. It contains four main parts: (i) background on the main definitions of entropy, (ii) statement and application of Jaynes' maximum entropy principle, (iii) statement and applications of the so-called inverse maximum entropy principle and (iv) statement and applications of maximum entropy principle involving generalized definitions of entropies. The personal contribution of the authors is (iii) in which, loosely speaking, they look for constraints which maximize entropy. It is a scholarly book, and a reader who is only slightly aware of Jaynes' maximum entropy principle will learn nothing.
The book is easy to read, clear, concise, contains many illustrative examples, and is nicely printed. However, despite its purpose, this book is much too incomplete. The reference list is incomplete. It is a deliberate choice of the authors to refer the reader to a previous book by one of them for a full bibliography on the topics, but it is a defect in the present one. The examples are misleading in their simplicity, and the book should comment on the nonlinear programming problem involved in the practical determination of the Lagrange parameters. There are many other problems in many fields of application which can be solved by means of the maximum entropy principle, and it would have been nice to write a small chapter, just to summarize them with the appropriate references. Let us mention a few such fields: artificial intelligence, linear and nonlinear filtering, self-organization, problems of spatial pattern formation, laser theory, maximum entropy principle applied to dynamic systems, and so on. (MathSciNet)

Bibliogr. p. 401-404. Notes bibliogr. Index