The book provides a broad introduction to both the theory and the
application of optimization with a special emphasis on the elegance,
importance, and usefulness of the parametric self-dual simplex method.
The book assumes that a problem in "standard form," is a problem with
inequality constraints and nonnegative variables. The main new
innovation to the book is the use of clickable links to the (newly
updated) online app to help students do the trivial but tedious
arithmetic when solving optimization problems.
The latest edition now includes: a discussion of modern Machine Learning
applications, as motivational material; a section explaining Gomory Cuts
and an application of integer programming to solve Sudoku problems.
Readers will discover a host of practical business applications as well
as non-business applications. Topics are clearly developed with many
numerical examples worked out in detail. Specific examples and concrete
algorithms precede more abstract topics.
With its focus on solving practical problems, the book features free C
programs to implement the major algorithms covered, including the
two-phase simplex method, the primal-dual simplex method, the
path-following interior-point method, and and the homogeneous self-dual
method. In addition, the author provides online tools that illustrate
various pivot rules and variants of the simplex method, both for linear
programming and for network flows. These C programs and online pivot
tools can be found on the book's website. The website also includes new
online instructional tools and exercises.
