Numerical optimization: theoretical and practical aspects

Abstract

This book is about the theoretical foundations of optimization algorithms, and also provides practical insights on how such methods should be implemented and applied. The goal of this text is not focused on in-depth details of state-of-the-art methods, but rather to provide a good foundation of the tried and trusted methods and how they can be used to solve real-world problems efficiently. The target audience for the text seems to be graduate students and engineers in industry as a good reference or self-study. However, it does not lend itself to easy adaption in a classroom setting due to the fact that only some chapters have problem sets and most chapters do not have a summary section. The book has four main parts each written by the one of the different authors. Two of the parts deal with standard unconstrained and constrained optimization techniques. The other two section deal with more complicated issues including solving problems that exhibit nonsmooth behavior and interior point methods. Solving optimization problems that have nonsmooth objectives or constraints is a formidable challenge because sensitivity information cannot be calculated using traditional approaches; the book provides a variety of ways to approach such problems. Interior point methods have been gaining popularity in the engineering optimization community for their efficiency and ability to maintain feasibility throughout the optimization process. There have been many textbooks written on the subject of numerical optimization. This book has the same flavor as many of these past books. A book with a very similar title by Nocedal and Wright [1] covered much of the same material, but it did not address nonsmooth problems. A classical book in the field by Flecther [2] considers nonsmooth problems but not interior point methods. Also, if one is more interested in comparing the performance of the various methods applied to engineering design problems, the book by Vanderplaats [3] may be more suitable. The appeal of this book is in the authors’ attention to detail and their advice on practical implementation issues. For many of the different optimization algorithms detailed flow charts are given. They also provide adequate examples to help the reader understand the methods better and explore possible pitfalls. There are, however, a few downsides of this book. The main one is that through translation of the book to English, it is evident that some of the finer points were lost and in some cases the text is hard to understand. The book could also have benefited from more figures; there are only 26. Finally, each of the dif