This textbook on Linear and Nonlinear Optimization is intended for
graduate and advanced undergraduate students in operations research and
related fields. It is both literate and mathematically strong, yet
requires no prior course in optimization. As suggested by its title, the
book is divided into two parts covering in their individual chapters LP
Models and Applications; Linear Equations and Inequalities; The Simplex
Algorithm; Simplex Algorithm Continued; Duality and the Dual Simplex
Algorithm; Postoptimality Analyses; Computational Considerations;
Nonlinear (NLP) Models and Applications; Unconstrained Optimization;
Descent Methods; Optimality Conditions; Problems with Linear
Constraints; Problems with Nonlinear Constraints; Interior-Point
Methods; and an Appendix covering Mathematical Concepts. Each chapter
ends with a set of exercises.
The book is based on lecture notes the authors have used in numerous
optimization courses the authors have taught at Stanford University. It
emphasizes modeling and numerical algorithms for optimization with
continuous (not integer) variables. The discussion presents the
underlying theory without always focusing on formal mathematical proofs
(which can be found in cited references). Another feature of this book
is its inclusion of cultural and historical matters, most often
appearing among the footnotes.
"This book is a real gem. The authors do a masterful job of rigorously
presenting all of the relevant theory clearly and concisely while
managing to avoid unnecessary tedious mathematical details. This is an
ideal book for teaching a one or two semester masters-level course in
optimization - it broadly covers linear and nonlinear programming
effectively balancing modeling, algorithmic theory, computation,
implementation, illuminating historical facts, and numerous interesting
examples and exercises. Due to the clarity of the exposition, this book
also serves as a valuable reference for self-study."
Professor Ilan Adler,
IEOR Department,
UC Berkeley
"A carefully crafted introduction to the main elements and applications
of mathematical optimization. This volume presents the essential
concepts of linear and nonlinear programming in an accessible format
filled with anecdotes, examples, and exercises that bring the topic to
life. The authors plumb their decades of experience in optimization to
provide an enriching layer of historical context. Suitable for advanced
undergraduates and masters students in management science, operations
research, and related fields."
Michael P. Friedlander,
IBM Professor of Computer Science,
Professor of Mathematics,
University of British Columbia
