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.