Linear and nonlinear optimization. (English) Zbl 06754912

Cottle, Richard W.; Thapa, Mukund N.

International Series in Operations Research & Management Science 253. New York, NY: Springer (ISBN 978-1-4939-7053-7/hbk; 978-1-4939-7055-1/ebook). xxxi, 614 p. (2017).

Preliminary review / Publisher’s description: 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.

MSC:

90-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming
90C05	Linear programming
90C30	Nonlinear programming

Keywords:

operations research; linear programming; mathematical programming; optimization models; nonlinear programming