Convex Functions, Monotone Operators and Differentiability

摘要: These notes start with an introduction to the differentiability of convex functions on Banach spaces, leading study Asplund spaces and their intriguing relationship monotone operators (and more general set-values maps) Radon-Nikodym property. While much this is classical, some it presented using streamlined proofs which were not available until recently. Considerable attention paid contemporary results variational principles perturbed optimization in exhibiting close connections spaces. An introductory course functional analysis adequate background for reading these can serve as basis a seminar one-term graduate course. There are numerous excercises, many form integral part exposition.