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**Robust optimization.**
*(English)*
Zbl 1221.90001

Princeton Series in Applied Mathematics. Princeton, NJ: Princeton University Press (ISBN 978-0-691-14368-2/hbk). xxii, 542 p. (2009).

This book is devoted to the robust approach to optimization problems, which actually means that we consider the worst case for an unknown parameter. Though the idea is not new, the authors of the book brought major contributions to the field by showing that in certain cases, the worst case can be reformulated in the class for which an algorithm with polynomial complexity (usually an interior-point algorithm) exists.

The book presents these kind of results but also some of the significant advances of the last years: (i) the “globalized robust counterpart” that takes into account the large deviations of the uncertain parameter; (ii) the safe tractable approximations of the robust problem, to be used when the latter has no polynomial complexity; (iii) the approximation of chance constraints; (iv) the dynamic, or multi stage approximation.

The book gives an extensive view of the main results in the field. Since these results involve complicated expressions (such as matrices built with many blocks) some parts of the book may require a high concentration from the reader. Overall, this reference book gives an excellent and stimulating account of the classical and advanced results in the field, and should be consulted by all researchers and practitioners.

The book presents these kind of results but also some of the significant advances of the last years: (i) the “globalized robust counterpart” that takes into account the large deviations of the uncertain parameter; (ii) the safe tractable approximations of the robust problem, to be used when the latter has no polynomial complexity; (iii) the approximation of chance constraints; (iv) the dynamic, or multi stage approximation.

The book gives an extensive view of the main results in the field. Since these results involve complicated expressions (such as matrices built with many blocks) some parts of the book may require a high concentration from the reader. Overall, this reference book gives an excellent and stimulating account of the classical and advanced results in the field, and should be consulted by all researchers and practitioners.

Reviewer: Joseph Frédéric Bonnans (Le Chesnay)