For students in industrial and systems engineering (ISE) and operations research (OR) to understand optimization at an advanced level, they must first grasp the analysis of algorithms, computational complexity, and other concepts and modern developments in numerical methods. Satisfying this prerequisite, Numerical Methods and Optimization: An Introduction combines the materials from introductory numerical methods and introductory optimization courses into a single text. This classroom-tested approach enriches a standard numerical methods syllabus with optional chapters on numerical optimization and provides a valuable numerical methods background for students taking an introductory OR or optimization course.
The first part of the text introduces the necessary mathematical background, the digital representation of numbers, and different types of errors associated with numerical methods. The second part explains how to solve typical problems using numerical methods. Focusing on optimization methods, the final part presents basic theory and algorithms for linear and nonlinear optimization.
The book assumes minimal prior knowledge of the topics. Taking a rigorous yet accessible approach to the material, it includes some mathematical proofs as samples of rigorous analysis but in most cases, uses only examples to illustrate the concepts. While the authors provide a MATLAB® guide and code available for download, the book can be used with other software packages.
In The Press
"The book is in most parts very well developed and is served by nice illustrations, a fluid style of writing, and a layout that makes it easy to read. … [it will] serve well its purpose of bridging the gap between numerical analysis, operations research, and mathematical optimization for undergraduate students in the applied sciences."
—Mathematical Reviews, August 2014
"If you are looking for an enjoyable and useful introduction to the basic topics of numerical methods and optimization, this is the right text to read. The authors are not only experienced lecturers but also active researchers in this area. They present the basic topics of numerical methods and optimization in an easy-to-follow, yet rigorous manner. In particular, they gently introduce some important topics, such as computational complexity, which are usually unavailable in textbooks on optimization for engineers. The authors occasionally turn to mathematical humor (such as ‘There are 10 types of people—those who understand binary, and those who don't’) to illustrate some material in the text. This informal contact with the reader exemplifies the engaging style of exposition characteristic of this excellent book."
—Oleg Burdakov, Linkoeping University, Sweden