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The Basics of Practical Optimization

Adam B. Levy
Publication Date: 
Number of Pages: 
[Reviewed by
Tom Schulte
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This introductory text is aimed at undergraduate students who have taken a multivariable calculus course. No knowledge of matrix basics is assumed. Concepts from matrix notation and multiplication to the Hessian are all introduced and explained in a self-contained manner.

The Basics of Practical Optimization initiates the reader into the practicalities of modeling and optimization with five classic examples: Yes/No Choices, Blending, Scheduling, Assignment, and Partitioning. These examples are detailed and solved completely. From there, the author takes us through the meat of the matter in several chapters comparing and contrasting the taxonomy of basic, practical optimization methods that grow out of Newton’s Method. This includes a focus on stopping conditions, how methods can fail, and ranking methods by convergence rate. Constraints are discussed in various contexts, including penalty methods and variable reduction.

Special emphasis is given to linear programs and their duals as well as sequential quadratic programming (SQP) with the Lagrangian Function. Another focus, covering an entire chapter, is integer programs and their application to networks.

Good for self-study or a course text, this work has short exercises small enough to do quickly during study (or in class) to reinforce key points. Longer problems are provided for more in depth study, or homework. There are plenty of computational problems and a few implementation projects for larger homework, computer labs, or group activities to be done over a longer period of time. These Implementations are specially supported through Mathematica notebooks that can be requested through the book’s web site.

Tom Schulte teaches finite mathematics at Oakland Community College in Michigan.