Convex Functions and Their Applications

Description

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, and it can also be used as a reference text for graduate courses on convex functions and applications. Front Matter ....Pages i-xvii Convex Functions on Intervals (Constantin P. Niculescu, Lars-Erik Persson)....Pages 1-70 Convex Sets in Real Linear Spaces (Constantin P. Niculescu, Lars-Erik Persson)....Pages 71-106 Convex Functions on a Normed Linear Space (Constantin P. Niculescu, Lars-Erik Persson)....Pages 107-184 Convexity and Majorization (Constantin P. Niculescu, Lars-Erik Persson)....Pages 185-226 Convexity in Spaces of Matrices (Constantin P. Niculescu, Lars-Erik Persson)....Pages 227-254 Duality and Convex Optimization (Constantin P. Niculescu, Lars-Erik Persson)....Pages 255-300 Special Topics in Majorization Theory (Constantin P. Niculescu, Lars-Erik Persson)....Pages 301-326 Back Matter ....Pages 327-415