Nonlinear programming.
3rd edition.

*(English)*Zbl 1360.90236
Belmont, MA: Athena Scientific (ISBN 978-1-886529-05-2/hbk). xviii, 861 p. (2016).

The aim of this book is to provide the readers an up-to-date, comprehensive, and rigorous account of nonlinear programming at the beginning graduate student level with fundamental concepts, the underlying principles, wide range of applications and various methods of solutions. This book is a nice combination of classical topics and new important recent developments. The overall structure of the book has not changed in the third edition. However, new material was included, some of the old material was discarded, a large amount of material was reorganized or revised.

The third edition of this book is divided into seven chapters. The first two chapters are devoted to unconstrained Optimization. Chapter 3 discusses constrained optimization problems and the methods of this chapter are based on iterative descent along suitably obtained directions. Chapter 4 and 5 are devoted to Lagrange multiplier theory and algorithms. Duality and Convex Programming are discussed in Chapter 6 and Dual Methods are presented in Chapter 7. The author nicely covers some of the important recent developments. Additional materials are provided in appendices on mathematical background, convex analysis, line search methods and implementation of Newton’s method. The book contains nice examples and exercises that are included at the end of each section of the chapter to enhance the reader’s understanding of the topic. All major proofs are given in full length which in my opinion increases the value of this book as a reference. Each chapter ends with a section of notes and sources, which is very interesting, well written and extremely useful for the readers.

The author develops the material from basic concepts and attempts to make accessible a number of topics that are not often found in textbooks. In the entire book, the presentation style is very clear, unique, compact and easy to follow, but at the same time mathematically rigorous. All the algorithms are clearly explained and presented. The organization of the book makes it possible to use it both as a textbook and as a reference book. Researchers as well as professionals in applied mathematics will also find this book very useful. Overall, this book is an excellent contribution to the field of optimization, and it is highly recommended to the students and researchers in Nonlinear Programming.

The third edition of this book is divided into seven chapters. The first two chapters are devoted to unconstrained Optimization. Chapter 3 discusses constrained optimization problems and the methods of this chapter are based on iterative descent along suitably obtained directions. Chapter 4 and 5 are devoted to Lagrange multiplier theory and algorithms. Duality and Convex Programming are discussed in Chapter 6 and Dual Methods are presented in Chapter 7. The author nicely covers some of the important recent developments. Additional materials are provided in appendices on mathematical background, convex analysis, line search methods and implementation of Newton’s method. The book contains nice examples and exercises that are included at the end of each section of the chapter to enhance the reader’s understanding of the topic. All major proofs are given in full length which in my opinion increases the value of this book as a reference. Each chapter ends with a section of notes and sources, which is very interesting, well written and extremely useful for the readers.

The author develops the material from basic concepts and attempts to make accessible a number of topics that are not often found in textbooks. In the entire book, the presentation style is very clear, unique, compact and easy to follow, but at the same time mathematically rigorous. All the algorithms are clearly explained and presented. The organization of the book makes it possible to use it both as a textbook and as a reference book. Researchers as well as professionals in applied mathematics will also find this book very useful. Overall, this book is an excellent contribution to the field of optimization, and it is highly recommended to the students and researchers in Nonlinear Programming.

Reviewer: Samir Kumar Neogy (New Delhi)

##### MSC:

90C30 | Nonlinear programming |

90-02 | Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming |