Convex Functions, Monotone Operators and Differentiability (Lecture Notes in Mathematics)

The improved and expanded second edition containsexpositions of some major results which have been obtainedin the years since the 1st edition.Theaffirmative answer by Preiss of the decades old questionof whether a Banachspace with an equivalent Gateauxdifferentiable norm is a weak Asplund space.The startlingly simple proof by Simons of Rockafellar'sfundamental maximal monotonicity theorem forsubdifferentials of convex functions.The exciting new version of the useful Borwein-Preiss smoothvariational principle due to Godefroy, Deville and Zizler.The material is accessible to students who have had a coursein Functional Analysis; indeed, the first edition has beenused in numerous graduate seminars. Starting with convexfunctions on the line, it leads to interconnected topics inconvexity, differentiability and subdifferentiability ofconvex functions in Banach spaces, generic continuity ofmonotone operators, geometry of Banach spaces and theRadon-Nikodym property, convex analysis, variationalprinciples and perturbed optimization.While much of this is classical, streamlined proofs foundmore recently are given in many instances. There arenumerous exercises, many of which form an integral part ofthe exposition.Phelps, R.R. is the author of 'Convex Functions, Monotone Operators and Differentiability (Lecture Notes in Mathematics)', published 1993 under ISBN 9783540567158 and ISBN 3540567151.