Bernd Heidergott – författare

Trains pull into a railroad station and must wait for each other before leaving again in order to let passengers change trains. How do mathematicians then calculate a railroad timetable that accurately reflects their comings and goings? One approach is to use max-plus algebra, a framework used to model Discrete Event Systems, which are well suited to describe the ordering and timing of events. This is the first textbook on max-plus algebra, providing a concise and self-contained introduction to the topic. Applications of max-plus algebra abound in the world around us. Traffic systems, computer communication systems, production lines, and flows in networks are all based on discrete even systems, and thus can be conveniently described and analyzed by means of max-plus algebra. The book consists of an introduction and thirteen chapters in three parts. Part One explores the introduction of max-plus algebra and of system descriptions based upon it. Part Two deals with a real application, namely the design of timetables for railway networks. Part Three examines various extensions, such as stochastic systems and min-max-plus systems.The text is suitable for last-year undergraduates in mathematics, and each chapter provides exercises, notes, and a reference section.

An introduction to gradient-based stochastic optimization that integrates theory and implementationThis book explains gradient-based stochastic optimization, exploiting the methodologies of stochastic approximation and gradient estimation. Although the approach is theoretical, the book emphasizes developing algorithms that implement the methods. The underlying philosophy of this book is that when solving real problems, mathematical theory, the art of modeling, and numerical algorithms complement each other, with no one outlook dominating the others.The book first covers the theory of stochastic approximation including advanced models and state-of-the-art analysis methodology, treating applications that do not require the use of gradient estimation. It then presents gradient estimation, developing a modern approach that incorporates cutting-edge numerical algorithms. Finally, the book culminates in a rich set of case studies that integrate the concepts previously discussed into fully worked models. The use of stochastic approximation in statistics and machine learning is discussed, and in-depth theoretical treatments for selected gradient estimation approaches are included.Numerous examples show how the methods are applied concretely, and end-of-chapter exercises enable readers to consolidate their knowledge. Many chapters end with a section on “Practical Considerations” that addresses typical tradeoffs encountered in implementation. The book provides the first unified treatment of the topic, written for a wide audience that includes researchers and graduate students in applied mathematics, engineering, computer science, physics, and economics.

An introduction to gradient-based stochastic optimization that integrates theory and implementationThis book explains gradient-based stochastic optimization, exploiting the methodologies of stochastic approximation and gradient estimation. Although the approach is theoretical, the book emphasizes developing algorithms that implement the methods. The underlying philosophy of this book is that when solving real problems, mathematical theory, the art of modeling, and numerical algorithms complement each other, with no one outlook dominating the others.The book first covers the theory of stochastic approximation including advanced models and state-of-the-art analysis methodology, treating applications that do not require the use of gradient estimation. It then presents gradient estimation, developing a modern approach that incorporates cutting-edge numerical algorithms. Finally, the book culminates in a rich set of case studies that integrate the concepts previously discussed into fully worked models. The use of stochastic approximation in statistics and machine learning is discussed, and in-depth theoretical treatments for selected gradient estimation approaches are included.Numerous examples show how the methods are applied concretely, and end-of-chapter exercises enable readers to consolidate their knowledge. Many chapters end with a section on ';Practical Considerations' that addresses typical tradeoffs encountered in implementation. The book provides the first unified treatment of the topic, written for a wide audience that includes researchers and graduate students in applied mathematics, engineering, computer science, physics, and economics.