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.
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