Linear Optimization

The Simplex Algorithm.- Geometry.- The Duality Theorem.- Matrix Environment.- General Form.- Unsolvable Systems.- Geometry Revisited.- Game Theory.- Network Environment.- Combinatorics.- Economics.- Integer Optimization.

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)