The aim of this book, as stated by the author, is to bridge the gap between textbooks that lack the required mathematical rigor (those primarily for management science courses) and textbooks for graduate-level courses that pay a lot of attention to the mathematical aspects and much less to computation and applications. To achieve this goal, the author uses the well-known software Maple to present some simple but effective implementations of the algorithms discussed in the text, as well as to produce graphical illustrations and figures.

The book is organized into two parts and includes four appendices. The appendices discuss specific projects in linear and nonlinear programming, and provide the necessary background in linear algebra and Maple.

Part 1 (chapters 1 to 5) is devoted to linear programming and integer linear programming. After chapter 1’s introduction to linear programming and the graphical solution of two-dimensional problems, chapter 2 presents the simplex method, first in tabular form and later in matrix form. I particularly appreciated the final section on interior point methods. Network optimization problems are presented in chapter 3, while duality and sensitivity analyses are discussed in chapter 4. The benefit of using software such as Maple is particularly evident in Section 4.2, where the user is unburdened of all the difficulties of the calculation, while still being able to perform symbolic operations. The first part ends with a chapter on integer linear programming.

Part 2 (chapters 6 to 8) is devoted to nonlinear programming. Chapter 6 discusses optimality conditions, and the remaining two chapters are devoted to unconstrained and constrained optimization.

The goal of the book--to combine mathematical rigor and attention to numerical aspects and applications in linear and nonlinear programming--is definitely ambitious. Using software that is able to perform symbolic calculations appears to be a correct approach to this difficult task. However, I am not convinced that the goal has been fully reached. The way the material is presented is not very suitable for a graduate-level course, and some portions are too technical for undergraduates. Clearly, it’s impossible to cover all possible aspects of linear and nonlinear programming in around 400 pages, but the author’s decisions to not include some aspects are not entirely convincing. Part 1 should devote less attention to the simplex method in tabular form, and instead introduce the reader directly to the simplex method in revised form. The decision to include a chapter on network optimization and integer programming is detrimental to both topics, due to the limited space that can be devoted to them. Part 2 presents the Levenberg-Marquardt algorithm, but not conjugate gradients and quasi-Newton methods. Penalty methods are not discussed at all in constrained nonlinear programming.

In conclusion, while the book is an interesting attempt to offer a textbook on linear and nonlinear programming that is suitable for both undergraduate and graduate students, and is mathematically rigorous and pays specific attention to computational aspects and applications, its goals have not been completely achieved. However, the textbook can be useful if it’s appropriately complemented with material specific to undergraduate and graduate students.