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© 2010

Linear Optimization

The Simplex Workbook

Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages 1-14
  2. Glenn H. Hurlbert
    Pages 1-27
  3. Glenn H. Hurlbert
    Pages 29-57
  4. Glenn H. Hurlbert
    Pages 59-72
  5. Glenn H. Hurlbert
    Pages 73-87
  6. Glenn H. Hurlbert
    Pages 89-105
  7. Glenn H. Hurlbert
    Pages 107-118
  8. Glenn H. Hurlbert
    Pages 119-128
  9. Glenn H. Hurlbert
    Pages 129-143
  10. Glenn H. Hurlbert
    Pages 145-162
  11. Glenn H. Hurlbert
    Pages 163-181
  12. Glenn H. Hurlbert
    Pages 183-194
  13. Glenn H. Hurlbert
    Pages 195-208
  14. Glenn H. Hurlbert
    Pages 209-229
  15. Back Matter
    Pages 1-41

About this book

Introduction

This undergraduate textbook is written for a junior/senior level course on linear optimization. Unlike other texts, the treatment allows the use of the "modified Moore method" approach by working examples and proof opportunities into the text in order to encourage students to develop some of the content through their own experiments and arguments while reading the text. Additionally, the focus is on the mathematics underlying the ideas of optimizing linear functions under linear constraints and the algorithms used to solve them. In particular, the author uses the Simplex Algorithm to motivate these concepts. The text progresses at a gentle and inviting pace. The presentation is driven by numerous examples and illustrations. Ample exercises are provided at the end of each chapter for mastering the material. Opportunities for integrating Maple (or similar) software are included in the book. The author’s own WebSim software can be freely downloaded from his website for pedagogical use.

The teacher's version of the text contains solutions embedded within the text, rather than in an appendix. It also has extra material and suggestions for the teacher’s benefit. Junior/senior level undergraduate students will benefit from the book, as will beginning graduate students. Future secondary school mathematics teachers will also find this book useful.

Arizona State University Professor Glenn H. Hurlbert has published nearly 50 articles in graph theory, combinatorics, and optimization, and has been the recipient of numerous teaching and mentoring awards from ASU, the ASU Parents Association, the School of Mathematical and Statistical Sciences, and the Mathematical Association of America.

Keywords

Convex Geometry Convexity Duality Linear Programming Networks Simplex Algorithm algorithms game theory integer optimization linear optimization matrix games modified Moore method optimization

Authors and affiliations

  1. 1.School of Mathematical and Arizona State UniversityTempeU.S.A.

Bibliographic information

Industry Sectors
Finance, Business & Banking

Reviews

From the reviews:

“In an effort at reform, Hurlbert (Arizona State) dubs his subject ‘linear optimization’ … . the author designs his work for discovery-based learning. … Ideally, this volume offers students the opportunity to recapitulate the Socratic process for reinforcement … . Summing Up: Recommended. Lower-division undergraduates.” (D. V. Feldman, Choice, Vol. 47 (9), May, 2010)

“Hurlbert’s textbook focuses on the mathematics of linear programming and important connections to linear algebra, graph theory, convexity, and game theory. The author has adopted the Moore method in which students are given some basic terminology and definitions and are then asked to develop the subject by proving a series of theorems. … This textbook would be very suitable for an undergraduate course in linear programming that uses the Moore method.” (Brian Borchers, The Mathematical Association of America, February, 2010)

“This text is … oriented toward duality as central to solving and understanding linear optimization problems. … Sequential steps in the ‘Workouts’ help guide the student through the discovery process. … this book would be an excellent choice for an instructor wishing to teach linear optimization to a motivated class. There is enough in here to sustain every taste and approach and create an excellent first course in optimization.” (Steven R. Dunbar, SIAM Review, Vol. 53 (3), 2011)