Convex Functions on Intervals -- Convex Sets in Real Linear Spaces -- Convex Functions on a Normed Linear Space -- Convexity and Majorization
-- Convexity in Spaces of Matrices -- Duality and Convex Optimization -- Special Topics in Majorization Theory -- A. Generalized Convexity on
Intervals -- B. Background on Convex Sets -- C. Elementary Symmetric Functions -- D. Second Order Differentiability of Convex Functions -- E.
The Variational Approach of PDE

This second edition provides a thorough introduction to contemporary convex function theory with many new results. A large variety of
subjects are covered, from the one real variable case to some of the most advanced topics. The new edition includes considerably more
material emphasizing the rich applicability of convex analysis to concrete examples. Chapters 4, 5, and 6 are entirely new, covering important
topics such as the Hardy-Littlewood-Pólya-Schur theory of majorization, matrix convexity, and the Legendre-Fenchel-Moreau duality theory.
This book can serve as a reference and source of inspiration to researchers in several branches of mathematics and engineering, an...