A Gentle Introduction to Optimization

Desire to improve drives many human activities. Optimization can be seen as a means for identifying better solutions by utilizing a scientific and mathematical approach. In addition to its widespread applications, optimization is an amazing subject with very strong connections to many other subjects and deep interactions with many aspects of computation and theory. The main goal of this textbook is to provide an attractive, modern, and accessible route to learning the fundamental ideas in optimization for a large group of students with varying backgrounds and abilities. The only background required for the textbook is a first-year linear algebra course (some readers may even be ready immediately after finishing high school). However, a course based on this book can serve as a header course for all optimization courses. As a result, an important goal is to ensure that the students who successfully complete the course are able to proceed to more advanced optimization courses.

Another goal of ours was to create a textbook that could be used by a large group of instructors, possibly under many different circumstances. To a degree, we tested this over a four-year period. Including the three of us, 12 instructors used the drafts of the book for two different courses. Students in various programs (majors), including accounting, business, software engineering, statistics, actuarial science, operations research, applied mathematics, pure mathematics, computational mathematics, computer science, combinatorics and optimization, have taken these courses. We believe that the book will be suitable for a wide range of students (mathematics, mathematical sciences including computer science, engineering including software engineering, and economics).