Convex Functions, Monotone Operators and Differentiability

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This expanded edition contains expositions of some major results which have been obtained recently, including the proof by Simons of Rockafellar’s fundamental maximal monotonicity theorem for sub-differentials of convex functions. The material is accessible to students who have had a course in functional analysis. Starting with convex functions on the line, it leads to interconnected topics in convexity, differentiability and sub-differentiability of convex functions in Banach spaces, the generic continuity of monotone operators, the geometry of Banach spaces and the Radon-Nikodyn property, convex analysis, variational principles and perturbed optimization.