Fundamentals of Convex Analysis and Optimization: A Supremum Function Approach

This book provides an innovative approach to convex analysis and optimization,based on an in-depth study of the behavior and properties of the supremum of families of convex functions. It offers a unifying methodology and provides an alternative or complementary view to the traditional approach, making it suitable for courses on optimization, convex and variational analysis, and other applications.

Format: Hardback
Length: 444 pages
Publication date: 03 August 2023
Publisher: Springer International Publishing AG

This comprehensive textbook delves into the realm of convex analysis and optimization, offering a fresh and innovative approach within the framework of these mathematical disciplines. Through an in-depth exploration of the behavior and properties of the supremum of families of convex functions, the book aims to provide a novel and systematic treatment of convex analysis. It encompasses a wide range of standard results and enhanced calculus rules in subdifferential analysis, offering a comprehensive coverage of the field.

The tools provided in the text facilitate a direct approach to the mathematical foundations of convex optimization, particularly focusing on optimality and duality theory. Additionally, the book explores various applications, including convexification processes in optimization, non-convex integration of the Fenchel subdifferential, variational characterizations of convexity, and the study of Chebychev sets.

What sets this textbook apart is its unique methodology, which unifies various concepts and operations while simultaneously emphasizing their underlying geometrical significance. The book also presents an alternative or complementary perspective to the traditional teaching of convex analysis, making it accessible to both graduate and post-graduate students in mathematics, as well as students in economics and engineering.

With its extensive coverage and rigorous analysis, this textbook serves as an invaluable resource for courses on optimization, convex and variational analysis. It is designed to cater to the needs of graduate and post-graduate students, as well as students in economics and engineering, who seek to gain a deep understanding of these mathematical concepts and their applications. The book also provides a solid foundation for courses on optimal control, data science, operations research, and economics (game theory), among other related fields.

For experts in functional analysis, convex geometry, and researchers interested in applying their work to real-world problems, this textbook represents a challenging and motivating development. It offers a wealth of knowledge and insights that can enhance their understanding and expertise in these areas.

Dimension: 235 x 155 (mm)
ISBN-13: 9783031295508
Edition number: 1st ed. 2023