**Pure and Applied Undergraduate Texts**

Volume: 30;
2017;
327 pp;
Hardcover

MSC: Primary 46; 65; 90; 97; 58; 11; 68;

Print ISBN: 978-1-4704-4114-2

Product Code: AMSTEXT/30

List Price: $69.00

AMS Member Price: $55.20

MAA Member Price: $62.10

**Electronic ISBN: 978-1-4704-4342-9
Product Code: AMSTEXT/30.E**

List Price: $69.00

AMS Member Price: $55.20

MAA Member Price: $62.10

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#### Supplemental Materials

# Mathematics of Optimization: How to do Things Faster

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*Steven J. Miller*

Optimization Theory is an active area of research with numerous applications; many of the books are designed for engineering classes, and thus have an emphasis on problems from such fields. Covering much of the same material, there is less emphasis on coding and detailed applications as the intended audience is more mathematical. There are still several important problems discussed (especially scheduling problems), but there is more emphasis on theory and less on the nuts and bolts of coding. A constant theme of the text is the “why” and the “how” in the subject. Why are we able to do a calculation efficiently? How should we look at a problem? Extensive effort is made to motivate the mathematics and isolate how one can apply ideas/perspectives to a variety of problems. As many of the key algorithms in the subject require too much time or detail to analyze in a first course (such as the run-time of the Simplex Algorithm), there are numerous comparisons to simpler algorithms which students have either seen or can quickly learn (such as the Euclidean algorithm) to motivate the type of results on run-time savings.

#### Readership

Undergraduate and graduate students interested in learning and teaching optimization and operation research.

#### Reviews & Endorsements

I think that this book offers a vast and useful outline of many mathematical problems arising from the common ground of optimization theory and operations research. Surely it can be useful and of interest to advanced undergraduates and beginning graduate students concerned with applications of mathematics to optimization problems and related fields.

-- Giorgio Giorgi, Mathematical Reviews

I started reading "Mathematics of Optimization: How to do Things Faster" without a significant background in optimization, linear programming, or operations research. Hence, I really did not know what to expect from the book. I was pleasantly surprised to find the book to be so much fun to work through. The writing is upbeat, entertaining and enlightening and the mathematics is varied, interesting, and inspiring...I am really impressed by "Mathematics of Optimization," and I would love to teach a course based on this book just in order to spend more time going through it myself...I think that the book is unique and should be relevant and of interest to advanced undergraduate and beginning graduate students in pure and applied mathematics and some closely related areas.

-- Jason M. Graham, MAA Reviews

#### Table of Contents

# Table of Contents

## Mathematics of Optimization: How to do Things Faster

- Cover Cover11
- Title page iii4
- Contents vii8
- Acknowledgements xiii14
- Preface xv16
- Course Outlines xix20
- Part 1 . Classical Algorithms 124
- Part 2 . Introduction to Linear Programming 4568
- Chapter 3. Introduction to Linear Programming 4770
- Chapter 4. The Canonical Linear Programming Problem 6790
- 4.1. Real Analysis Review 6891
- 4.2. Canonical Forms and Quadratic Equations 7093
- 4.3. Canonical Forms in Linear Programming: Statement 7194
- 4.4. Canonical Forms in Linear Programming: Conversion 7396
- 4.5. The Diet Problem: Round 2 7598
- 4.6. A Short Theoretical Aside: Strict Inequalities 7699
- 4.7. Canonical is Not Always Best 77100
- 4.8. The Oil Problem 78101
- 4.9. Exercises 79102

- Chapter 5. Symmetries and Dualities 83106
- Chapter 6. Basic Feasible and Basic Optimal Solutions 95118
- Chapter 7. The Simplex Method 107130

- Part 3 . Advanced Linear Programming 119142
- Chapter 8. Integer Programming 121144
- 8.1. The Movie Theater Problem 122145
- 8.2. Binary Indicator Variables 125148
- 8.3. Logical Statements 126149
- 8.4. Truncation, Extrema and Absolute Values 128151
- 8.5. Linearizing Quadratic Expressions 130153
- 8.6. The Law of the Hammer and Sudoku 131154
- 8.7. Bus Route Example 134157
- 8.8. Exercises 135158

- Chapter 9. Integer Optimization 143166
- Chapter 10. Multi-Objective and Quadratic Programming 153176
- Chapter 11. The Traveling Salesman Problem 161184
- Chapter 12. Introduction to Stochastic Linear Programming 169192

- Part 4 . Fixed Point Theorems 177200
- Part 5 . Advanced Topics 253276
- Back Cover Back Cover1353