The Basics of Practical Optimization

Contents: Preface. 1. Modeling. 2. Impractical Optimization. 3. Basic Practical Optimization. 4. Some Practical Modifications. 5. How Methods Are Ranked. 6. Constraints. 7. More Practical Modifications. 8. Integer Variables. 9. Other Methods. Appendices. Bibliography. Index. This textbook provides undergraduate students with an introduction to optimization and its uses for relevant and realistic problems. The only prerequisite for readers is a basic understanding of multivariable calculus because additional materials, such as explanations of matrix tools, are provided in a series of Asides both throughout the text at relevant points and in a handy appendix. The book presents: step-by-step solutions for five prototypical examples that fit the general optimization model, instruction on using numerical methods to solve models and making informed use of the results, information on how to optimize while adjusting the method to accommodate various practical concerns, three fundamentally different approaches to optimizing functions under constraints, and ways to handle the special case when the variables are integers. The author provides four types of learn-by-doing activities throughout the book: Exercises meant to be attempted as they are encountered and that are short enough for in-class use Problems for lengthier in-class work or homework Computational Problems for homework or a computer lab session Implementations usable as collaborative activities in the computer lab over extended periods of time This textbook is appropriate for undergraduate students who have taken a multivariable calculus course. Keywords: optimization; linear programming; applied mathematics; modelling; numerical methods.…