Ferrera J. An Introduction to Nonsmooth Analysis

Elsevier Inc., 2013. — 164 pages. ISBN: 0128007311 | ISBN13: 9780128007310.
Nonsmooth Analysis is a relatively recent area of mathematical analysis. The literature about this subject consists mainly in research papers and books. The purpose of this book is to provide a handbook for undergraduate and graduate students of mathematics that introduce this interesting area in detail.
Includes different kinds of sub and super differentials as well as generalized gradients.
Includes also the main tools of the theory, as Sum and Chain Rules or Mean Value theorems.
Content is introduced in an elementary way, developing many examples, allowing the reader to understand a theory which is scattered in many papers and research books.Basic concepts and results
Convex Functions
The subdifferential of a Convex function
The subdifferential. General case
Calculus
Lipschitz functions and the generalized gradient
Applications