An Introduction to Nonsmooth Analysis

This is a handbook for undergraduate and graduate students of mathematics that introduces the emerging area of mathematical analysis known as Nonsmooth Analysis

Juan Ferrera (Author)

9780128007310, Elsevier Science

Paperback, published 26 November 2013

164 pages
22.9 x 15.1 x 1.2 cm, 0.23 kg

"...starting from the very beginning, adopting a slow, easy to follow linear development and reaching to a self-contained theory...oriented towards undergraduate students, as a first quick introduction to the topic." --MathSciNet

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.

1. Basic concepts and results: Upper and lower limits. Semicontinuity. Differentiability. Two important Theorems.2. Convex Functions: Convex sets and convex functions. Continuity of convex functions. Separation Results. Convexity and Differentiability. 3. The subdifferential of a Convex function: Subdifferential properties. Examples.4. The subdifferential. General case: Definition and basic properties. Geometrical meaning of the subdifferential. Density of subdifferentiability points. Proximal subdifferential 5. Calculus: Sum Rule. Constrained minima. Chain Rule. Regular functions: Elementary properties. Mean Value results. Decreasing Functions 6. Lipschitz functions and the generalized gradient: Lipschitz regular functions. The generalized gradient. Generalized Jacobian. Graphical derivative 7. Applications: Flow invariant sets. Viscosity solutions. Solving equations.

Subject Areas: Geometry [PBM], Numerical analysis [PBKS], Calculus & mathematical analysis [PBK]