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Nonlinear optimization with engineering applications. (English) Zbl 1167.90001
Springer Optimization and Its Applications 19. New York, NY: Springer (ISBN 978-0-387-78722-0/hbk). xvi, 280 p. (2008).
This book gives on 280 pages a broad overview of nonlinear optimization. The presented methods include direct search techniques, the steepest descend approach, trust region methods as well as Newton and quasi-Newton techniques with globalization strategies for the unconstrained case. For constrained optimization problems penalty approaches, SQP methods, barrier techniques and interior point methods are discussed. Additionally, the book covers several topics as line search approaches, filter methods and the computation of derivatives. The presented optimization approaches are compared with each other by means of several examples with up to 200 variables. The numerical results are mostly obtained by the software package OPTIMA written by the author. The book contains 25 chapters with an average of 11 pages. Due to the variety of considered solution techniques, the presentation of each method and its theoretical analysis is rather brief. Nevertheless, the introduction of the different techniques is written in a very comprehensible way. Furthermore, each section contains exercises to verify and deepen the understanding of the material.

MSC:
90-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming
90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
Software:
OPTIMA
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