Introduction to Methods for Nonlinear Optimization

This book provides a concise introduction to nonlinear optimization methods and collects and organizes selected important topics on optimization algorithms, making it suitable for graduate or upper undergraduate students and advanced courses. It also includes a review of the essential mathematical background.

Format: Paperback / softback
Length: 723 pages
Publication date: 04 June 2023
Publisher: Springer International Publishing AG

This comprehensive book serves two primary objectives:

• To provide a concise and comprehensive introduction to nonlinear optimization methods, suitable for use as a textbook at the graduate or upper undergraduate level.
• To gather and organize selected important topics on optimization algorithms that are often overlooked in textbooks, offering valuable material for advanced courses and serving as a valuable reference text for self-study and research.

The book is structured into three distinct blocks of chapters:

• The first block focuses on the basic theory and optimality conditions of optimization. It includes short chapters that present the most essential results in theory and algorithms, tailored to suit the needs of introductory courses.
• The second block delves into unconstrained and constrained optimization techniques. These topics are covered in depth, with each chapter presenting the key concepts and methodologies in a clear and concise manner.
• The third block addresses methods that are increasingly being employed to tackle complex optimization problems. Difficulty in solving these problems can arise from factors such as high nonlinearity, ill-conditioning of the Hessian matrix, limited information on first-order derivatives, and the need to handle large-scale problems.

Throughout the book, various key subjects are addressed, including:

• Exact penalty functions and exact augmented Lagrangian functions, which play a crucial role in formulating and solving optimization problems.
• Nonmonotone methods, which are particularly useful in dealing with non-convex optimization problems.
• Decomposition algorithms, which break down complex optimization problems into smaller subproblems for easier solution.
• Derivative-free methods, which are gaining popularity for solving nonlinear equations and optimization problems without relying on derivatives.

In addition to these core topics, the book includes appendices that provide a comprehensive review of the essential mathematical background required for understanding nonlinear optimization. This review covers topics such as convex analysis, which can be valuable as part of an introductory course in optimization.

With its extensive coverage, rigorous analysis, and practical applications, this book is an invaluable resource for students, researchers, and practitioners in the field of optimization. It serves as a valuable companion for anyone seeking to deepen their understanding of nonlinear optimization techniques and apply them to real-world problems.

Weight: 1369g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031267895
Edition number: 1st ed. 2023