In a revised edition, this book presents basic results of the theory of convex sets and functions in infinite-dimensional spaces. Includes new results on advanced concepts of subdifferential for convex functions and new duality results in convex programming.

An updated and revised edition of the 1986 title Convexity and Optimization in Banach Spaces, this book provides a self-contained presentation of basic results of the theory of convex sets and functions in infinite-dimensional spaces. The main emphasis is on applications to convex optimization and convex optimal control problems in Banach spaces. A distinctive feature is a strong emphasis on the connection between theory and application. This edition has been updated to include new results pertaining to advanced concepts of subdifferential for convex functions and new duality results in convex programming. The last chapter, concerned with convex control problems, has been rewritten and completed with new research concerning boundary control systems, the dynamic programming equations in optimal control theory and periodic optimal control problems. Finally, the structure of the book has been modified to highlight the most recent progression in the field including fundamental results on the theory of infinite-dimensional convex analysis and includes helpful bibliographical notes at the end of each chapter.

This book provides a strong emphasis on the link between abstract theory and applications to convex optimization Chapters end with an informative 'bibliographic notes' section for further reading Includes fundamental results of infinite-dimensional convex analysis Includes supplementary material: sn.pub/extras

Autorentext

Viorel Barbu is professor of Mathematics at Alexandru Ioan Cuza University (Romania) and also member of Romanian Academy and of European Academy of Science. He has published several monographs and textbooks on nonlinear analysis, infinite dimensional optimization, partial differential equations and Navier-Stokes equations with Springer, Academic Press, Kluwer, Birkhauser. Michael Röckner is professor of Mathematics at Bielefeld University (Germany) and a distinguished visiting professor at CAS. He is a member of the Academia Europaea, the Academy of Sciences and Literature, Mainz, and a foreign honorary member of the Romanian Academy. His main areas of research are stochastic analysis, in particular, stochastic partial differential equations, the theory of Dirichlet forms and potential theory. He is a coauthor of several monographs in these fields.

Klappentext

An updated and revised edition of the 1986 title Convexity and Optimization in Banach Spaces , this book provides a self-contained presentation of basic results of the theory of convex sets and functions in infinite-dimensional spaces. The main emphasis is on applications to convex optimization and convex optimal control problems in Banach spaces. A distinctive feature is a strong emphasis on the connection between theory and application.

This edition has been updated to include new results pertaining to advanced concepts of subdifferential for convex functions and new duality results in convex programming. The last chapter, concerned with convex control problems, has been rewritten and completed with new research concerning boundary control systems, the dynamic programming equations in optimal control theory and periodic optimal control problems.

Finally, the structure of the book has been modified to highlight the most recent progression in the field including fundamental results on the theory of infinite-dimensional convex analysis and includes helpful bibliographical notes at the end of each chapter.

Inhalt

Fundamentals of Functional Analysis.- Convex Functions.- Convex Programming.- Convex Control Problems in Banach Spaces.