Anyone wanting to publish a book in a respectable and classical research field needs to find a niche to justify the originality. This statement includes the area of mathematical optimization, which interests Kochenderfer and Wheeler. They decided to focus on the algorithmic perspective dealing with automatic methods of optimization. Their approach is successful. What’s more, they present a number of examples developed in the Julia programming language. This way, even beginners are given not only a broad selection of topics in the area, but they are additionally provided with live illustrations or tools to be used at once.

The selection of topics is generally not surprising, although the number covered (that is, many) is notable. Focus shifts toward stochastic aspects, which is not that typical. The topics covered include the following groups: optimization based on derivatives (chapters 1, 2, 4, and 5), the optimization of functions of one variable (chapters 1 through 7), nondeterministic heuristics (chapters 8 and 9), constrained optimization with duality and Lagrangian methods (chapter 10), linear programming (chapters 11 and 19), optimization with more than one criteria (chapter 12), methods based on evaluated data points (chapters 13 through 16), uncertainty programming (chapters 17 and 18), methods based on formal grammars (chapter 20), and methods that simultaneously support many engineering fields (chapter 21). The book ends with appendices on the Julia language (Appendix A), testing function for optimization algorithms (Appendix B), a refresher on various background mathematical concepts (Appendix C), and solutions to chapter exercises (Appendix D).

The book’s originality stems from its broad scope, clearly presented, with an emphasis on topics that are not commonly covered (especially the ones given in chapters 13 through 20). Notably, many new results are given. Although the book starts with the basics, the knowledge provided is ultimately quite deep. Therefore, this is a book for anybody trained in calculus, algebra, and probability. Since the flow assumes an accumulation of knowledge, it is good to read the work linearly. This way will certainly satisfy laypeople, but also readers fluent in optimization due to the many interesting details.

While not strictly aimed at computer specialists, readers interested in extending their knowledge on many important mathematical ideas behind system design or machine learning will find Kochenderfer and Wheeler’s work useful. The referenced papers alone include seminal works from various computer science subfields.

Nevertheless, the book can be also treated as a fully fledged textbook on optimization theory or numerical methods. The provided exercises and code listings are very supportive from this viewpoint. On the other hand, there are very few examples of optimization for real-life problems. Apparently, this is done on purpose. First, the book is not aimed at any specific engineering field. Second, it lets the authors focus on algorithmic aspects of the presented issues.

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