Algorithmic Principles of Mathematical Programming investigates the
mathematical structures and principles underlying the design of
efficient algorithms for optimization problems. Recent advances in
algorithmic theory have shown that the traditionally separate areas of
discrete optimization, linear programming, and nonlinear optimization
are closely linked. This book offers a comprehensive introduction to the
whole subject and leads the reader to the frontiers of current research.
The prerequisites to use the book are very elementary. All the tools
from numerical linear algebra and calculus are fully reviewed and
developed. Rather than attempting to be encyclopedic, the book
illustrates the important basic techniques with typical problems. The
focus is on efficient algorithms with respect to practical usefulness.
Algorithmic complexity theory is presented with the goal of helping the
reader understand the concepts without having to become a theoretical
specialist. Further theory is outlined and supplemented with pointers to
the relevant literature.
The book is equally suited for self-study for a motivated beginner and
for a comprehensive course on the principles of mathematical programming
within an applied mathematics or computer science curriculum at advanced
undergraduate or graduate level. The presentation of the material is
such that smaller modules on discrete optimization, linear programming,
and nonlinear optimization can easily be extracted separately and used
for shorter specialized courses on these subjects.
