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An Introduction to Optimization

Edwin K. P. Chong and Stanislaw H. Żak
John Wiley
Publication Date: 
Number of Pages: 
Discrete Mathematics and Optimization
[Reviewed by
Ita Cirovic Donev
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There are many introductory books out there on optimization. However, when one needs to decide which one to use, lots of questions and problems arise. Many of these books are very narrow minded, i.e. they only present some theory and expect the reader to fill in the rest, leaving lots of gaps. This book is different. It falls into a smaller group of introductory books on optimization that is actually useful to the reader. It guides and leads the reader through the learning path.

An Introduction to Optimization starts out with a mathematical overview of the topics such as vector spaces, transformations, geometry and calculus. All of the main concepts are presented in a lucid style. Theorems are accompanied with full proofs. There are also some examples scattered throughout the text. Reading Part I takes us back to those school days when we took the first/second year courses. It allows the reader to slowly recollect the memories of the theorems and methods. Further understanding should come easily by completing the exercises. Part I serves as an adequate introduction and a refresher for the rest of the book.

The main part of the book is divided into three main sections covering methods of unconstrained optimization, linear programming and nonlinear constrained optimization. Even though the style of presentation is formal, there is no loss of clarity as the authors continue to discuss the methods in a narrative way with numerous illustrations and detailed examples. The proofs are quite detailed and easy to follow.

This is indeed an introductory book as the authors concentrate to explain the methods in the most accessible way. You will not find too much hand waiving in this book. As such it could easily be used for self study.

The style of the book can be described as user friendly. Examples are stated very clearly and the results are presented with attention to detail. The examples do a good job of illustrating the theory presented. Even some trivial computations are presented, which should be a big plus for the students.

Numerous exercises are given at the end of each chapter and are divided into theoretical and applied ones. They start out as easy calculations, to get the reader going, followed by harder problems. The applied ones require the use of the MATLAB computing software. Overall, the book has a good ratio of examples and theory.

Given that students would benefit the most from this book, one of the negative aspects is that there is no MATLAB (or any other) code presented. Given the detailed presentation, however, readers should find it easy to write their own MATLAB code using the algorithms presented.

Ita Cirovic Donev holds a Masters degree in statistics from Rice University. Her main research areas are in mathematical finance; more precisely, statistical methods for credit and market risk. Apart from the academic work she does statistical consulting work for financial institutions in the area of risk management.


Part I: Mathematical Review.

1. Methods of Proof and Some Notation.

2. Vector Spaces and Matrices.

3. Transformations.

4. Concepts from geometry.

5. Elements of Calculus.

Part II: Unconstrained Optimization.

6. Basics of Set-Constrained and Unconstrained Optimization.

7. One-Dimensional Search Methods.

8. Gradient Methods.

9. Newton's Method.

10. Conjugate Direction Methods.

11. Quasi-Newton Methods.

12. Solving Linear Equations.

13. Unconstrained Optimization and Neural Networks.

14. Global Search Algorithms.

Part III: Linear Programming.

15. Introduction to Linear Programming.

16. Simplex Method.

17. Duality.

18. Nonsimplex Methods.

Part IV: Nonlinear Constrained Optimization

19. Problems with Equality Constraints.

20. Problems with Inequality Constraints.

21. Convex Optimization Problems.

22. Algorithms for Constrained Optimization.

23. Multiobjective Optimization.