Linear and Nonlinear Programming

The 5th edition of this classic textbook covers the central concepts of practical optimization techniques, with an emphasis on methods that are both state-of-the-art and popular. It is organized into three parts: Part I offers a self-contained introduction to linear programming, Part II covers the theory of unconstrained optimization, and Part III extends the concepts to constrained optimization problems. New to this edition are popular topics in data science and machine learning.

Format: Paperback / softback
Length: 609 pages
Publication date: 02 November 2022
Publisher: Springer Nature Switzerland AG

The fifth edition of this renowned textbook delves into the core principles of practical optimization techniques, placing a strong emphasis on both state-of-the-art and widely adopted methods. A significant revelation emerges from the connection between the purely analytical nature of an optimization problem and the behavior of algorithms employed to solve it. Each chapter concludes with comprehensive end-of-chapter exercises to reinforce the learning process.

The content is structured into three distinct sections. Part I serves as a self-contained introduction to linear programming, presenting the fundamental elements of the underlying theory, numerous efficient numerical algorithms, and numerous significant special applications. Part II, entirely independent of Part I, delves into the theory of unconstrained optimization, encompassing the derivation of appropriate optimality conditions and an introduction to fundamental algorithms. This section explores the general properties of algorithms and introduces various notions of convergence. Part III extends the concepts developed in the second part to constrained optimization problems, with the exception of a few isolated sections. As such, Parts II and III can be utilized independently of Part I, and the book has been successfully employed in this manner at numerous universities.

This edition introduces several popular topics in data science and machine learning, including the Markov Decision Process, Farkas lemma, convergence speed analysis, duality theories and applications, various first-order methods, stochastic gradient method, mirror-descent method, Frank-Wolf method, ALM/ADMM method, interior trust-region method for non-convex optimization, distributionally robust optimization, online linear programming, and more.

By incorporating these new topics, the textbook remains at the forefront of optimization research, equipping readers with the latest tools and techniques to address complex optimization problems in various fields.

Weight: 946g
Dimension: 155 x 233 x 43 (mm)
ISBN-13: 9783030854522
Edition number: 5th ed. 2021