Linear and Nonlinear Programming

This textbook offers an in-depth exploration of optimization techniques, including both linear and nonlinear programming methods, making it an essential resource for students and professionals.

The 5th edition of Linear and Nonlinear Programming presents a comprehensive overview of practical optimization techniques, focusing on both state-of-the-art and widely used methods. A key insight of this edition is the relationship between the analytical nature of optimization problems and the algorithms designed to solve them. Each chapter concludes with exercises that reinforce the concepts discussed, making it a valuable resource for students and practitioners alike.

The content is structured into three distinct parts. Part I provides an introduction to linear programming, covering essential theoretical elements, effective numerical algorithms, and key applications. This section is designed to be self-contained, ensuring that readers can grasp the foundational aspects of linear programming without prior knowledge. Part II shifts focus to unconstrained optimization theory, detailing optimality conditions and introducing fundamental algorithms. It also investigates the characteristics of algorithms and various convergence concepts. Part III builds on the principles established in Part II, addressing constrained optimization problems, and is designed to be independent from Part I, allowing for flexible reading.

This edition also introduces contemporary topics relevant to data science and machine learning, including the Markov Decision Process, Farkas’ lemma, and various advanced methods such as stochastic gradient and interior trust-region methods. The inclusion of these topics ensures that Linear and Nonlinear Programming remains relevant in today's rapidly evolving landscape of optimization techniques.